Shangyou Zhang Publication

Preprint/unpublished (but referenced by some published papers):

• Invertible Jacobian for hexahedral finite elements. Part 1. Bijectivity(5/2005)

• Invertible Jacobian for hexahedral finite elements. Part 2. global positivity(5/2005)

• Subtetrahedral test for the positive Jacobian of hexahedral elements (11/2005)

• On a nested refinement of anisotropic tetrahedral grids under Hessian metrics (12/2006)

• Bases for C0-P1 divergence-free elements and for C1-P2 finite elements on union jack grids (6/2008,6/2009)

• 2015-elas  A FAMILY OF CONFORMING MIXED FINITE ELEMENTS FOR LINEAR ELASTICITY ON TRIANGULAR GRIDS

 Journal papers: (Stored on Google Drive)

  Shown on MATH REVIEWS (8/27/2025) : 

1. 1. 2025-i-w   Wang, Chunmei; Zhang, Shangyou An auto-stabilized weak Galerkin method for elasticity interface problems on nonconvex meshes. J. Comput. Appl. Math. 473 (2026), Paper No. 116854, 17 pp.  

   2. 2025-l-c  Zeng, Yuping; Zhang, Shangyou; A medius error analysis for the conforming discontinuous Galerkin finite element methods. J. Numer. Math. 33 (2025), no. 3, 267–287.  

   3.  2025-p32  Xu, Xuejun; Zhang, Shangyou A nonconforming P3+B4 and discontinuous P2 mixed finite element on tetrahedral grids. Adv. Comput. Math. 51 (2025), no. 4, Paper No. 30, 13 pp

   4. 2025-c1k   Zhang, Shangyou A family of P4 macro-bubble enriched C1-Pk finite elements on triangular meshes. Numer. Math. 157 (2025), no. 3, 1133–1159. 

   5. 2025-p2   Zhang, Shangyou A nonconforming P2 and discontinuous P1 mixed finite element on tetrahedral grids. Adv. Appl. Math. Mech. 17 (2025), no. 4, 1259–1274. 

   6. 2025-b-s   Zhang, Shangyou Stabilizing the Scott-Vogelius elements by Guzman-Neilan bubble functions on triangular meshes. J. Appl. Math. Comput. 71 (2025), no. 3, 3625–3643. 

   7.  2025-bell  Xu, Xuejun; Zhang, Shangyou; Three families of C1-P2m+1 Bell finite elements on triangular meshes. Numer. Algorithms 99 (2025), no. 2, 717--734.

   8. 2025-s-b  Zeng, Yuping; Zhang, Shangyou; A robust Morley type conforming discontinuous Galerkin method for a fourth order singular perturbation problem. ZAMM Z. Angew. Math. Mech. 105 (2025), no. 5, Paper No. e70083.

   9. 2025-wgst  Wang, Chunmei; Zhang, Shangyou; Auto-stabilized weak Galerkin finite element methods for Stokes equations on non-convex polytopal meshes. J. Comput. Phys. 533 (2025), Paper No. 114006. 

   10. 2025-rk   Pan, Mengjiao; Zhang, Jingjing; Zhang, Shangyou; Three sixth-order explicit symplectic Runge–Kutta-Nystrom methods with exact parameters. Results Appl. Math. 26 (2025), Paper No. 100568.  

   11.  2025-dfcdg Ye, Xiu; Zhang, Shangyou; A divergence-free Pk CDG finite element for the Stokes equations on triangular and tetrahedral meshes. Numer. Math. Theory Methods Appl. 18 (2025), no. 1, 157--174. 

   12.  2025-dd     Liang, Qigang; Xu, Xuejun; Zhang, Shangyou; On a sharp estimate of overlapping Schwarz methods in  H(curl; Ω) and H(div; Ω), IMA J. Numer. Anal. 45 (2025), no. 2, 1009--1027.

   13. 2025-2hd  Huang, Yunqing; Xu, Xuejun; Zhang, Shangyou; A P2 H-div nonconforming-H-curl finite element for the Stokes equations on triangular meshes, Comput. Methods Appl. Math. 25 (2025), no. 2, 459--473.

   14.  2025-l Zeng, Yuping; Zhang, Shangyou; Low regularity error estimates of three pressure-robust discontinuous Galerkin methods for stokes equations, ESAIM Math. Model. Numer. Anal. 59 (2025), no. 2, 873--898. 

   15.  2025-wm  Wang, Chunmei; Zhang, Shangyou Efficient weak Galerkin finite element methods for Maxwell equations on polyhedral meshes without convexity constraints. J. Comput. Appl. Math. 465 (2025), Paper No. 116575, 21 pp.

   16. 2025-rm  Zhang, Shangyou; Zhang, Zhimin; A Locking-Free and Reduction-Free Conforming Finite Element Method for the Reissner-Mindlin Plate on Rectangular Meshes, Commun. Appl. Math. Comput. 7 (2025), no. 2, 470--484. 

   17. 2025-p3  Zhang, Shangyou; Conforming P3 divergence−free finite elements for the Stokes equations on subquadrilateral triangular meshes,   Commun. Appl. Math. Comput. 7 (2025), no. 2, 426--441.

   18.  2025-c2  Ye, Xiu; Zhang, Shangyou; Constructing a CDG Finite Element with Order Two Superconvergence on Rectangular Meshes,    Commun. Appl. Math. Comput. 7 (2025), no. 2, 411--425.

   19. 2025-heat  Gao, Fuzheng; Zhang, Shangyou;   An explicit superconvergent weak Galerkin Galerkin  finite element method for the heat equation,   Adv. Appl. Math. Mech. 17 (2025), no. 2, 538--553.

   20. 2025-r-m Chen, Gang; Zhang, Lu; Zhang, Shangyou;  Locking-free HDG methods for Reissner–Mindlin plates equations on polygonal meshes,  J. Sci. Comput. 102 (2025), no. 3, Paper No. 67. 

   21. 2025-es Liu, Xiaojuan; Li, Maojun; Yin, Tao; Zhang, Shangyou; A nonsingular-kernel Dirichlet-to-Dirichlet mapping method for the exterior Stokes problem. Adv. Comput. Math. 51 (2025), no. 1, Paper No. 2.

1. 22.  2024-co  Lin, Yanping; Xu, Xuejun; Zhang, Shangyou; Superconvergent P1 honeycomb virtual elements and lifted P3 solutions. Calcolo 61 (2024), no. 4, Paper No. 67. 

   23. 2024-3c   Zhang, Shangyou; Three Low Order H-Curl-Curl Finite Elements on Triangular Meshes. Comput. Methods Appl. Math. 24 (2024), no. 4, 1021–1032. 

   24. 2024-c1p    Xu, Xuejun; Zhang, Shangyou; A C1-P7 Bell Finite Element on Triangle. Comput. Methods Appl. Math. 24 (2024), no. 4, 995–1000.

   25. 2024-mhd    Xu, Xuejun; Ye, Xiu; Zhang, Shangyou; A macro BDM H-div mixed finite element on polygonal and polyhedral meshes. Appl. Numer. Math. 206 (2024), 283–297.

   26. 2024-s-s    Mu, Lin; Ye, Xiu; Zhang, Shangyou; Zhu, Peng; A DG Method for the Stokes Equations on Tensor Product Meshes with [Pk]d−Pk−1 Element. Commun. Appl. Math. Comput. 6 (2024), no. 4, 2431–2454.

   27. 2024-la    Huang, Yunqing; Zhang, Shangyou; Locking-free Argyris–Lagrange finite elements for the Reissner–Mindlin plate. Calcolo 61 (2024), no. 3, Paper No. 49. 

   28. 2024-ct    Wang, Chunmei; Wang, Junping; Zhang, Shangyou; Weak Galerkin finite element methods for optimal control problems governed by second order elliptic equations. J. Comput. Appl. Math. 452 (2024), Paper No. 115982.

   29. 2024-ss   Wang, Junping; Wang, Xiaoshen; Ye, Xiu; Zhang, Shangyou; Zhu, Peng; On the superconvergence of a WG method for the elliptic problem with variable coefficients. Sci. China Math. 67 (2024), no. 8, 1899–1910.  

   30. 2024-t-sp     Xie, Ziqing; Zhang, Shangyou; On an accurate numerical integration for the triangular and tetrahedral spectral finite elements. Adv. Comput. Math. 50 (2024), no. 4, Paper No. 63, 17 pp.

   31. 2024-lrst      Zeng, Yuping; Zhong, Liuqiang; Wang, Feng; Cai, Mingchao; Zhang, Shangyou; Low regularity error analysis for an H(div)-conforming discontinuous Galerkin approximation of Stokes problem. J. Comput. Appl. Math. 451 (2024), Paper No. 116118, 14 pp.

   32. 2024v-s   Zeng, Yuping; Zhong, Liuqiang; Cai, Mingchao; Wang, Feng; Zhang, Shangyou Conforming and nonconforming virtual element methods for Signorini problems. J. Sci. Comput. 100 (2024), no. 1, Paper No. 18, 25 pp.

   33. 2024prst   Yang, Yan; Ye, Xiu; Zhang, Shangyou  A pressure-robust stabilizer-free WG finite element method for the Stokes equations on simplicial grids. Electron. Res. Arch. 32 (2024), no. 5, 3413–3432.

   34. 2024-p46     Zhang, Shangyou On the convergence of 2D P4+ triangular and 3D P6+ tetrahedral divergence-free finite elements. Numer. Methods Partial Differential Equations 40 (2024), no. 4, Paper No. e23088, 15 pp.

   35.  2024-pu     Huang, Yunqing; Zhang, Shangyou On the optimal order approximation of the partition of unity finite element method. CSIAM Trans. Appl. Math. 5 (2024), no. 2, 221–233.

   36.  2024-cwg      Li, Dan; Wang, Chunmei; Zhang, Shangyou Weak Galerkin methods for elliptic interface problems on curved polygonal partitions. J. Comput. Appl. Math. 450 (2024), Paper No. 115995, 15 pp.

   37.  2024-hD  Ye, Xiu; Zhang, Shangyou; An H-div finite element method for the Stokes equations on polytopal meshes. Comput. Appl. Math. 43 (2024), no. 4, Paper No. 184.

   38. 2024-mM    Wang, Chunmei; Ye, Xiu; Zhang, Shangyou; A modified weak Galerkin finite element method for the Maxwell equations on polyhedral meshes. J. Comput. Appl. Math. 448 (2024), Paper No. 115918.

   39. 2024-cp  Ye, Xiu; Zhang, Shangyou; A superconvergent CDG finite element for the Poisson equation on polytopal meshes. ZAMM Z. Angew. Math. Mech. 104 (2024), no. 3, Paper No. e202300521, 16 pp. 

   40. 2024-mRq  Xu, Liwei; Xu, Xuejun; Zhang, Shangyou A modified rotated-Q1 finite element for the Stokes equations on quadrilateral and hexahedral meshes. J. Sci. Comput. 99 (2024), no. 1, Paper No. 11, 19 pp. 

   41.  2024-ws  Zeng, Yuping; Zhong, Liuqiang; Wang, Feng; Zhang, Shangyou; Cai, Mingchao A pressure-robust numerical scheme for the Stokes equations based on the WOPSIP DG approach. J. Comput. Appl. Math. 445 (2024), Paper No. 115819, 13 pp.

   42.  2024-mo  Li, Dan; Wang, Chunmei; Wang, Junping; Zhang, Shangyou; High order Morley elements for biharmonic equations on polytopal partitions. J. Comput. Appl. Math. 443 (2024), 115757.  

   43.  2024-pa   Wang, Chunmei; Wang, Junping; Zhang, Shangyou A parallel iterative procedure for weak Galerkin methods for second order elliptic problems. Int. J. Numer. Anal. Model. 21 (2024), no. 1, 1–19. 

   44.  2024-ne   Zhang, Shangyou Neilan's divergence-free finite elements for Stokes equations on tetrahedral grids. Numer. Methods Partial Differential Equations 40 (2024), no. 1, Paper No. e24055, 27 pp. 

   45.  2024-2s   Ye, Xiu; Zhang, Shangyou; Order two superconvergence of the CDG finite elements for non-self adjoint and indefinite elliptic equations. Adv. Comput. Math. 50 (2024), no. 1, Paper No. 2. 

   46.  2024-hd    Zhang, Shangyou; Zhu, Peng BDM H(div) weak Galerkin finite element methods for Stokes equations. Appl. Numer. Math. 197 (2024), 307–321. 

   47.   2024-4b    Ye, Xiu; Zhang, Shangyou Four-order superconvergent CDG finite elements for the biharmonic equation on triangular meshes. J. Comput. Appl. Math. 440 (2024), Paper No. 115516, 13 pp. 

1. 48.  2023-bh   Ye, Xiu; Zhang, Shangyou A conforming DG method for the biharmonic equation on polytopal meshes. Int. J. Numer. Anal. Model. 20 (2023), no. 6, 855–869.  

   49.   2023-rk  Jun Zhang; Jingjing Zhang and Zhang, Shangyou   Explicit Symplectic Runge–Kutta–Nystr\"om Methods Based on Roots of Shifted Legendre Polynomial, Mathematics 11 (2023) no. (20), Paper 4291.

   50.  2023-nf-pl    Zhang, Shangyou; Robust Falk-Neilan Finite Elements for the Reissner-Mindlin Plate. Commun. Appl. Math. Comput. 5 (2023), no. 4, 1697–1712. 

   51. 2023-4WgBih     Ye, Xiu; Zhang, Shangyou; Four-Order Superconvergent Weak Galerkin Methods for the Biharmonic Equation on Triangular Meshes. Commun. Appl. Math. Comput. 5 (2023), no. 4, 1323–1338. 

   52. 2023-p1sp             Zhang, Shangyou A subspace of linear nonconforming finite element for nearly incompressible elasticity and Stokes flow. J. Numer. Math. 31 (2023), no. 3, 157–173.  

   53. 2023-p1b-s          Zhang, Shangyou A macro-bubble enriched P1-P0 finite element for the Stokes equations on triangular and tetrahedral meshes. Calcolo 60 (2023), no. 3, Paper No. 44, 20 pp. 

   54. 2023-exWG         Wang, Junping; Ye, Xiu; Zhang, Shangyou A time-explicit weak Galerkin scheme for parabolic equations on polytopal partitions. J. Numer. Math. 31 (2023), no. 2, 125–135. 

   55. 2023-porous      Bi, Chuan; Ou, Miao-Jung Yvonne; Zhang, Shangyou Integral representation of hydraulic permeability. Proc. Roy. Soc. Edinburgh Sect. A 153 (2023), no. 3, 907–936.  

   56. 2023-wg4c           Wang, Chunmei; Wang, Junping; Zhang, Shangyou Weak Galerkin finite element methods for quad-curl problems. J. Comput. Appl. Math. 428 (2023), Paper No. 115186, 13 pp. 

   57. 2023-cdg2t         Ye, Xiu; Zhang, Shangyou Order two superconvergence of the CDG finite elements on triangular and tetrahedral meshes. CSIAM Trans. Appl. Math. 4 (2023), no. 2, 256–274. 

   58. 2023-wg2sq        Ye, Xiu; Zhang, Shangyou Constructing order two superconvergent WG finite elements on rectangular meshes. Numer. Math. Theory Methods Appl. 16 (2023), no. 1, 230–241. 

   59. 2023-2sq-s5        Wang, Junping; Wang, Xiaoshen; Ye, Xiu; Zhang, Shangyou; Zhu, Peng Two-order superconvergence for a weak Galerkin method on rectangular and cuboid grids. Numer. Methods Partial Differential Equations 39 (2023), no. 1, 744–758. (Reviewer: Huanrong Li) 65N15 (65N30)

   60. 2023-elas           Wang, Xiuli; Meng, Xianglong; Zhang, Shangyou; Zhou, Huifang; A modified weak Galerkin finite element method for the linear elasticity problem in mixed form. J. Comput. Appl. Math. 420 (2023), Paper No. 114743. 

   61. 2023-if                Wang, Chunmei; Zhang, Shangyou; A weak Galerkin method for elasticity interface problems. J. Comput. Appl. Math. 419 (2023), Paper No. 114726.

1. 62. 2022cdg2S       Ye, Xiu; Zhang, Shangyou Order two superconvergence of the CDG method for the Stokes equations on triangle/tetrahedron. J. Appl. Anal. Comput. 12 (2022), no. 6, 2578–2592. 

   63. 2022-c0cdg-bh      Ye, Xiu; Zhang, Shangyou A C0 conforming DG finite element method for biharmonic equations on triangle/tetrahedron. J. Numer. Math. 30 (2022), no. 3, 163–172. 

   64.  2022-mixLap         Lin, Yanping; Ye, Xiu; Zhang, Shangyou A mixed finite-element method on polytopal mesh. Commun. Appl. Math. Comput. 4 (2022), no. 4, 1374–1385.  

   65.  2022-1dCDG       Ye, Xiu; Zhang, Shangyou; Achieving superconvergence by one-dimensional discontinuous finite elements: the CDG method. East Asian J. Appl. Math. 12 (2022), no. 4, 781–790.

   66. 2022-HdivDiv      Ye, Xiu; Zhang, Shangyou A family of H-div-div mixed triangular finite elements for the biharmonic equation. Results Appl. Math. 15 (2022), Paper No. 100318, 16 pp.

   67. 2022-ife               Tatyana Sorokina and Shangyou Zhang, An Interpolated Galerkin Finite Element Method for the Poisson Equation. J. Sci. Comput. 92 (2022), no. 2, Paper No. 47, 14 pp.

   68. 2022-hypSys       Zhang, Tie; Zhang, Shangyou An explicit weak Galerkin method for solving the first order hyperbolic systems. J. Comput. Appl. Math. 412 (2022), Paper No. 114311, 14 pp.

   69. 2022-1dWg           Ye, Xiu; Zhang, Shangyou Achieving superconvergence by one-dimensional discontinuous finite elements: weak Galerkin method. East Asian J. Appl. Math. 12 (2022), no. 3, 590–598.

   70. 2022-wdivBih      Ye, Xiu; Zhang, Shangyou A weak divergence CDG method for the biharmonic equation on triangular and tetrahedral meshes. Appl. Numer. Math. 178 (2022), 155–165.

   71. 2022-ldg               Ye, Xiu; Zhang, Shangyou; Zhu, Peng Development of a LDG method on polytopal mesh with optimal order of convergence. J. Comput. Appl. Math. 410 (2022), Paper No. 114179, 10 pp. 

   72. 2022-31             Gao, Fuzheng; Ye, Xiu; Zhang, Shangyou A discontinuous Galerkin finite element method without interior penalty terms. Adv. Appl. Math. Mech. 14 (2022), no. 2, 299–314.

   73. 2022-1 pdf           Feng, Yue; Liu, Yujie; Wang, Ruishu; Zhang, Shangyou; A stabilizer-free weak Galerkin finite element method for the stokes equations. Adv. Appl. Math. Mech. 14 (2022), no. 1, 181–201.

   74. pdf 2022-2          Wang, Xiaoshen; Ye, Xiu; Zhang, Shangyou; Zhu, Peng  A weak Galerkin least squares finite element method of Cauchy problem for Poisson equation. J. Comput. Appl. Math. 401 (2022), Paper No. 113767, 9 pp. 

1. 75. 2021-c0Bgrad      Ye, Xiu; Zhang, Shangyou; A C0-conforming DG finite element method for biharmonic equations on triangle/tetrahedron. J. Numer. Math. 30 (2021), no. 3, 163–172.

   76. pdf 2021-61          Ye, Xiu; Zhang, Shangyou A stabilizer free WG method for the Stokes equations with order two superconvergence on polytopal mesh. Electron. Res. Arch. 29 (2021), no. 6, 3609–3627. 

   77. pdf 2021-47           Wang, Xiaoshen; Ye, Xiu; Zhang, Shangyou Weak Galerkin finite element methods with or without stabilizers. Numer. Algorithms 88 (2021), no. 3, 1361–1381. 65N30 (65N12 65N15) 

   78. pdf 2021-62           Peng, Hui; Zhai, Qilong; Zhang, Ran; Zhang, Shangyou; A weak Galerkin-mixed finite element method for the Stokes-Darcy problem. Sci. China Math. 64 (2021), no. 10, 2357–2380.  

   79. pdf 2021-41          Mu, Lin; Ye, Xiu; Zhang, Shangyou Development of pressure-robust discontinuous Galerkin finite element methods for the Stokes problem. J. Sci. Comput. 89 (2021), no. 1, Paper No. 26, 25 pp.

   80. pdf 2021-43           Mu, Lin; Ye, Xiu; Zhang, Shangyou A stabilizer-free, pressure-robust, and superconvergence weak Galerkin finite element method for the Stokes equations on polytopal mesh. SIAM J. Sci. Comput. 43 (2021), no. 4, A2614–A2637. 

   81. pdf 2021-45            Ye, Xiu; Zhang, Shangyou; Low regularity error analysis for weak Galerkin finite element methods for second order elliptic problems. Numer. Math. Theory Methods Appl. 14 (2021), no. 3, 613–623. 

   82. pdf 2021-9          Wang, Chunmei; Wang, Junping; Ye, Xiu; Zhang, Shangyou de Rham complexes for weak Galerkin finite element spaces. J. Comput. Appl. Math. 397 (2021), Paper No. 113645, 11 pp. 

   83. pdf 2021-q          Xie, Ziqing; Zhang, Shangyou Accurate numerical integration for the quadrilateral and hexahedral finite elements. Numer. Methods Partial Differential Equations 37 (2021), no. 3, 2446–2457. 

   84. pdf 2021-59          Al-Taweel, Ahmed; Wang, Xiaoshen; Ye, Xiu; Zhang, Shangyou A stabilizer free weak Galerkin finite element method with supercloseness of order two. Numer. Methods Partial Differential Equations 37 (2021), no. 2, 1012–1029. 

   85. pdf 2021-8          Ye, Xiu; Zhang, Shangyou A numerical scheme with divergence free H−div triangular finite element for the Stokes equations. Appl. Numer. Math. 167 (2021), 211–217. 

   86. pdf 2021-7          Feng, Yue; Liu, Yujie; Wang, Ruishu; Zhang, Shangyou A conforming discontinuous Galerkin finite element method on rectangular partitions. Electron. Res. Arch. 29 (2021), no. 3, 2375–2389. 

   87. pdf 2021-6          Ye, Xiu; Zhang, Shangyou A conforming discontinuous Galerkin finite element method for the Stokes problem on polytopal meshes. Internat. J. Numer. Methods Fluids 93 (2021), no. 6, 1913–1928. 

   88. pdf 2021-5           Ye, Xiu; Zhang, Shangyou A new weak gradient for the stabilizer free weak Galerkin method with polynomial reduction. Discrete Contin. Dyn. Syst. Ser. B 26 (2021), no. 8, 4131–4145. 

   89. pdf 2021-h           Ye, Xiu; Zhang, Shangyou A stabilizer-free pressure-robust finite element method for the Stokes equations. Adv. Comput. Math. 47 (2021), no. 2, Paper No. 28, 17 pp. 

   90. pdf 2021-s2          Ye, Xiu; Zhang, Shangyou A stabilizer free weak Galerkin finite element method on polytopal mesh: Part II. J. Comput. Appl. Math. 394 (2021), Paper No. 113525, 11 pp. 

   91. pdf 2021-s3          Ye, Xiu; Zhang, Shangyou A stabilizer free weak Galerkin finite element method on polytopal mesh: Part III. J. Comput. Appl. Math. 394 (2021), Paper No. 113538, 9 pp. 

   92. pdf 2021-pl          Ye, Xiu; Zhang, Shangyou; A weak Galerkin finite element method for p-Laplacian problem. East Asian J. Appl. Math. 11 (2021), no. 2, 219–233. 

   93. pdf 2021-e            Zhang, Shangyou Erratum to "A C1-P2 finite element without nodal basis''. ESAIM Math. Model. Numer. Anal. 55 (2021), suppl., S877–S878. 

   94. pdf 2021-33         Cui, Ming; Ye, Xiu; Zhang, Shangyou A modified weak Galerkin finite element method for the biharmonic equation on polytopal meshes. Commun. Appl. Math. Comput. 3 (2021), no. 1, 91–105.

   95. pdf 2021-35         Ye, Xiu; Zhang, Shangyou A Pk+2 polynomial lifting operator on polygons and polyhedrons. Appl. Math. Lett. 116 (2021), Paper No. 107033, 6 pp. 

   96. pdf 2021-1           Ye, Xiu; Zhang, Shangyou; Zhu, Peng A weak Galerkin finite element method for nonlinear conservation laws. Electron. Res. Arch. 29 (2021), no. 1, 1897–1923.

1. 97. pdf 2020-30  Ye, Xiu; Zhang, Shangyou; Zhu, Yunrong; Stabilizer-free weak Galerkin methods for monotone quasilinear elliptic PDEs. Results Appl. Math. 8 (2020), Paper No. 100097, 10 pp. 

   98. pdf 2020   Ye, Xiu; Zhang, Shangyou A conforming discontinuous Galerkin finite element method: Part III. Int. J. Numer. Anal. Model. 17 (2020), no. 6, 794-805.

   99. pdf 2020   Ye, Xiu; Zhang, Shangyou; A Stabilizer Free Weak Galerkin Method for the Biharmonic Equation on Polytopal Meshes. SIAM J. Numer. Anal. 58 (2020), no. 5, 2572-2588.

   100. pdf 2020   Yin Yang; Jindi Wang; Shangyou Zhang; Emran Tohidi; Convergence analysis of space-time Jacobi spectral collocation method for solving time-fractional Schrödinger equations. Applied Mathematics and Computation 387 (2020) 124489.

   101. pdf 2020   Peng, Hui; Zhai, Qilong; Zhang, Ran; Zhang, Shangyou; Weak Galerkin and continuous Galerkin coupled finite element methods for the Stokes-Darcy interface problem. Commun. Comput. Phys. 28 (2020), no. 3, 1147-1175.

   102. pdf 2020   Hu, Jun; Tian, Shudan; Zhang, Shangyou; A family of 3D H2-nonconforming tetrahedral finite elements for the biharmonic equation. Sci. China Math. 63 (2020), no. 8, 1505-1522.

   103. pdf 2020-26 Gao, Fuzheng; Zhang, Shangyou; Zhu, Peng; Modified weak Galerkin method with weakly imposed boundary condition for convection-dominated diffusion equations. Appl. Numer. Math. 157 (2020), 490-504.

   104. 2020-table   Wang, Junping; Ye, Xiu; Zhang, Shangyou; Numerical investigation on weak Galerkin finite elements. Int. J. Numer. Anal. Model. 17 (2020), no. 4, 517-531.

   105. pdf 2020-20   Ye, Xiu; Zhang, Shangyou; Zhang, Zhimin A locking-free weak Galerkin finite element method for Reissner-Mindlin plate on polygonal meshes. Comput. Math. Appl. 80 (2020), no. 5, 906-916.

   106. pdf 2020-19   Runchang Lin, Xiu Ye, Shangyou Zhang and Peng Zhu; Analysis of a DG method for singularly perturbed convection-diffusion problems, Journal of Applied Analysis and Computation, 10 (2020), no. 3, 830-841.

   107. pdf 2020-18   Sorokina, Tatyana; Zhang, Shangyou; An inequality involving a triangle and an interior point and its application, Math. Inequal. Appl. 23 (2020), no. 2, 713-717.

   108. pdf 2020-24   Zhang, Tie; Zhang, Shangyou The weak Galerkin finite element method for the transport-reaction equation. J. Comput. Phys. 410 (2020), 109399, 13 pp.

   109. pdf 2020-26hu   Hu, Jun; Zhang, Shangyou; An error analysis method SPP-BEAM and a construction guideline of nonconforming finite elements for fourth order elliptic problems. J. Comput. Math. 38 (2020), no. 1, 195-222.

   110. pdf 2020-14   Sorokina, Tatyana; Zhang, Shangyou; Conforming and nonconforming harmonic finite elements. Appl. Anal. 99 (2020), no. 4, 569-584.

   111. pdf 2020-15   Zhai, Qilong; Tian, Tian; Zhang, Ran; Zhang, Shangyou; A symmetric weak Galerkin method for solving non-divergence form elliptic equations. J. Comput. Appl. Math. 372 (2020), 112693, 10 pp.

   112. pdf 2020-08   Ye, Xiu; Zhang, Shangyou; A stabilizer-free weak Galerkin finite element method on polytopal meshes. J. Comput. Appl. Math. 371 (2020), 112699.

   113. pdf 2020   Wang, Xiuli; Zhai, Qilong; Zhang, Ran; Zhang, Shangyou; The weak Galerkin finite element method for solving the time-dependent integro-differential equations. Adv. Appl. Math. Mech. 12 (2020), no. 1, 164-188.

   114. pdf 2020-13   Yin Yang, Jianyong Tao, Shangyou Zhang and Petr V. Sivtsev; A Jacobi collocation method for the fractional Ginzburg-Landau differential equation, Adv. Appl. Math. Mech., 12 (2020), no. 1, 57-86.

   115. pdf 2020-07   Cui, Ming; Zhang, Shangyou; On the Uniform Convergence of the Weak Galerkin Finite Element Method for a Singularly-Perturbed Biharmonic Equation. J. Sci. Comput. 82 (2020), no. 1, Art. 5, 15 pp.

   116. pdf 2020-03   Ye, Xiu; Zhang, Shangyou A conforming discontinuous Galerkin finite element method: Part II. Int. J. Numer. Anal. Model. 17 (2020), no. 2, 281-296.

   117. pdf 2020-05   Ye, Xiu; Zhang, Shangyou A conforming discontinuous Galerkin finite element method. Int. J. Numer. Anal. Model. 17 (2020), no. 1, 110-117.

   118. pdf 2020-06   Sorokina, Tatyana; Zhang, Shangyou Conforming harmonic finite elements on the Hsieh-Clough-Tocher split of a triangle. Int. J. Numer. Anal. Model. 17 (2020), no. 1, 54-67.

   119. pdf 2020-04   Ye, Xiu; Zhang, Shangyou; Zhu, Peng A discontinuous Galerkin least-squares method for div-curl systems. J. Comput. Appl. Math. 367 (2020), 112474, 10 pp.

   120. pdf 2020-2   Zhang, Tie; Zhang, Shangyou The weak Galerkin finite element method for the symmetric hyperbolic systems. J. Comput. Appl. Math. 365 (2020), 112375, 13 pp.

   121. pdf 2020-01   Ye, Xiu; Zhang, Shangyou; Zhang, Zhimin A new P1 weak Galerkin method for the biharmonic equation. J. Comput. Appl. Math. 364 (2020), 12337, 10 pp.

   122. pdf 2019-10   Hu, Jun; Zhang, Shangyou A cubic H3-nonconforming finite element. Commun. Appl. Math. Comput. 1 (2019), no. 1, 81-100.

   123. pdf 2019-09   Hu, Jun; Zhang, Shangyou; Zhang, Zhimin On the 2pth-order of convergence of the Galerkin difference method. SIAM J. Numer. Anal. 57 (2019), no. 5, 2189-2199.

   124.  pdf 2019-h    Yang, Yin; Qiao, Wanying; Wang, Jindi; Zhang, Shangyou; Spectral collocation methods for nonlinear coupled time fractional Nernst-Planck equations in two dimensions and its convergence analysis. Comput. Math. Appl. 78 (2019), no. 5, 1431-1449.

   125.   pdf 2019-g   Mu, Lin; Ye, Xiu; Zhang, Shangyou Development of a P2 element with optimal L2 convergence for biharmonic equation. Numer. Methods Partial Differential Equations 35 (2019), no. 4, 1497-1508.

   126.   pdf 2019-f  Duan, Huoyuan; Liu, Wei; Ma, Junhua; Tan, Roger C. E.; Zhang, Shangyou A family of optimal Lagrange elements for Maxwell's equations. J. Comput. Appl. Math. 358 (2019), 241-265.

   127.   2019-e   Huang, Yunqing; Li, Jichun; Zhang, Shangyou Continuous mixed finite elements for the second order elliptic equation with a low order term. J. Comput. Appl. Math. 357 (2019), 273-283.

   128.  2019-d    Duan, Huoyuan; Du, Zhijie; Liu, Wei; Zhang, Shangyou New mixed elements for Maxwell equations. SIAM J. Numer. Anal. 57 (2019), no. 1, 320-354.

   129. pdf   2019-c   Xu, Liwei; Zhang, Shangyou; Hsiao, George C. Nonsingular kernel boundary integral and finite element coupling method. Appl. Numer. Math. 137 (2019), 80-90.

   130. pdf   2019-b   Ye, Xiu; Zhang, Shangyou: A discontinuous least-squares finite-element method for second-order elliptic equations. Int. J. Comput. Math. 96 (2019), no. 3, 557-567.

   131. pdf   2019-a   Wang, Junping; Zhai, Qilong; Zhang, Ran; Zhang, Shangyou A weak Galerkin finite element scheme for the Cahn-Hilliard equation. Math. Comp. 88 (2019), no. 315, 211-235.

1. 132. pdf   2018-b   (with Runchang Lin, Texas A &M, Xiu Ye, Arkansas, and Peng Zhu, Jiaxing University) A weak Galerkin finite element method for singularly perturbed convection-diffusion-reaction problems. SIAM J. Numer. Anal. 56 (2018), no. 3, 1482-1497.

   133. pdf    2018-c  (with Jichun Li, University of Nevada, and Xiu Ye, Arkansas) A weak Galerkin least-squares finite element method for div-curl systems. J. Comput. Phys. 363 (2018), 79-86.

   134. pdf  2018-a   (With Lin Mu, Michigan State, Junping Wang, NSF, and Xiu Ye, Arkansas) A Discrete Divergence Free Weak Galerkin Finite Element method for the Stokes Equations, Appl. Numer. Math. 125 (2018), 172--182.

1. 135. pdf   2017-e   A P4 bubble enriched P3 divergence-free finite element on triangular grids, Comput. Math. Appl. 74 (2017), no. 11, 2710--2722.

   136. pdf   2017-d   (with Shuo Zhang, Chinese Academy of Science) C0P2-P0 Stokes finite element pair on sub-hexhadron tetrahedral grids, Calcolo 54 (2017), no. 4, 1403--1417.

   137.   2017-p2.pdf   (With Jun Hu, Peking University) A canonical construction of $H^m$-nonconforming triangular finite elements, Ann. Appl. Math., 33 (2017) no. 3, 266-288.

   138.    2017-c  (With Zhimin Zhang, Wayne State University and Qingsong Zou, Sun Yat-sen University) A post-processed flux conserving finite element solution, Numer. Methods Partial Differential Equations 33 (2017), no. 6, 1859--1883.

   139.    2017-a.pdf  (With Min Zhang, Sichuan University) A 3D conforming-nonconforming mixed finite element for solving symmetric-stress Stokes equations, Int. J. Numer. Anal. Model., 14 (2017), no. 4-5, 730--743.

   140. pdf 2017b  2017b.pdf  (with Wei Cai, University of North Carolina at Charlotte and Jun Hu, Peking University) High Order Hierarchical H(div) Constrained Transport Finite Element Method for MHD Magnetic Equation, Numer. Math. Theory Methods Appl. 10 (2017), no. 2, 243--254.

1. 141.  2016-a    (With Dejun Xie, South U of Sci. and Tech. China) A semi discrete model for mortgage valuation and its computation by an adaptive finite element method, Int. J. Num. Anal. Modeling, 13 (2016), no. 6, 831--851.

   142.   16-b   (With Jun Hu, Peking University) Finite element approximations of symmetric tensors on simplicial grids in $R^n$: the lower order case, Math. Models Methods Appl. Sci. 26 (2016), no. 9, 1649--1669.

   143.   2016-4d   A family of differentiable finite elements on simplicial grids in four space dimensions. ( Chinese ) Math. Numer. Sin. 38 (2016), no. 3, 309--324.

   144.   2016-d   (With Jun Hu, Peking University, Hongying Man, Beijing Institute of Technology, and Jianye Wang, Peking University) The simplest nonconforming mixed finite element method for linear elasticity in the symmetric formulation on $n$-rectangular grids, Comput. Math. Appl. 71 (2016), no. 7, 1317--1336.

   145.   2016-e   (With Mo Mu, Hong Kong University of Science and Technology) Stable $Q_k$-$Q_ k-1 $ mixed finite elements, J. Comput. Appl. Math. 301 (2016), 188--200.

   146. pdf  2016-f   Coefficient jump-independent approximation of the conforming and nonconforming finite element solutions, Adv. Appl. Math. Mech., 8 (2016) No. 5, 722--736.

1. 147.   2015-a   (With Lin Mu, Michigan State, Junping Wang, NSF, and Xiu Ye, Arkansas) A weak Galerkin finite element method for the Maxwell equations. J. Sci. Comput. 65 (2015), no. 1, 363--386.

   148.    2015-b  (With Jun Hu, Peking University) A family of symmetric mixed finite elements for linear elasticity on tetrahedral grids, Sci. China Math. 58 (2015), no. 2, 297--307.

   149.   2015-c   (With Chunmei Wang and Jinru Chen, Nanjing Normal University) A mass-preserving interpolation operator and an interpolated mortar condition for nonconforming finite elements, J. Sci. Comp., 62 (2015), no. 1, 179--197.

   150. pdf  2015-d   (With Jun Hu, Peking University) The minimal conforming $H^k$ finite element spaces on $R^n$ rectangular grids, Math. Comp. 84 (2015), no. 292, 563--579.

1. 151. pdf  2014-e    (With Lizhen Qin, Purdue University and Zhimin Zhang, Wayne State University) Finite Element Formulation in Flat Coordinate Spaces to Solve Elliptic Problems on General Closed Riemannian Manifolds, SIAM J. Sci. Comput. 36-5 (2014), A2149--A2165.

   152. pdf  2014-a   (With Wenbin Chen, Fudan University and Xuejun Xu, Chinese Academy of Science) On the Optimal Convergence Rate of a Robin-Robin Domain Decomposition Method, J. Comp. Math., 32 (2014), no. 4, 456--475.

   153. pdf  2014-c    (With Mingxia Li, China University of Geoscience, Shipeng Mao, Chinese Academy of Sciences) New error estimates of nonconforming mixed finite element methods for the Stokes problem, Mathematical Methods in the Applied Sciences, 37 (2014), no. 7, 931--951.

   154. pdf  2014-b   (With Lin Mu, Michigan State, Junping Wang, NSF, and Xiu Ye, Arkansas) A $C^0$-weak Galerkin finite element method for the biharmonic equation, J. Sci. Comp., 59 (2014), no. 2, 473-495.

   155. pdf   2014-d   (With George C. Hsiao, Delaware, and Liwei Xu, Chongqing University) Solving negative order equations by the multigrid method via variable substitution, J. Sci. Comp., 59 (2014), no. 2, 371-385.

   156. pdf   2014-0  (With Jun Hu, Peking University and Hongying Man, Beijing Institute of Technology) A simple conforming mixed finite element for linear elasticity on rectangular grids in any space dimension, J. Sci. Comp., 58 (2014), no. 2, 367-379.

1. 157. pdf  2013-e    (With Yunqing Huang, Xiangtan University) Supercloseness of the divergence-free finite element solutions on rectangular grids, Communications in Mathematics and Statistics, 1 (2013), 143-162.

   158. pdf   2013-c   (With Jun Hu, Peking University) Nonconforming finite element methods on quadrilateral meshes, SCIENCE CHINA Mathematics, 56 (2013), no. 12, 2599-2614.

   159. pdf  2013-a   (With Houde Han and Zhongyi Huang, Tsinghua University) An Iterative Method based on equation decomposition for the fourth-order singular perturbation problem, Numerical Methods for Partial Differential Equations, 29 (2013), no. 3, 961-978.

   160. pdf   2012   (With Jianguo Huang, Shanghai Jiao Tong University) A divergence-free finite element method for a type of 3D Maxwell equations, Applied Numerical Mathematics, 62 (2012), 802-813.

1. 161. pdf 2011-mg   (With Chuanmiao Chen, Hongling Hu, Ziqing Xie, Hunan Normal University) A jumping multigrid method via finite element extrapolation, Int. J. Numer. Anal. Model. Series B, 2 (2011), no. 4, 281-297.

   162. pdf  2011-ps3   Quadratic divergence-free finite elements on Powell-Sabin tetrahedral grids, Calcolo, 48 (2011), No 3, 211-244.

   163. pdf  2011-q2c1   (With Jun Hu, Peking University and Yunqing Huang, Xiangtan University) The lowest order differentiable finite element on rectangular grids, SIAM Num. Anal., 49 (2011), no. 4, 1350-1368.

   164. pdf   2011-drm   (With Constantin Bacuta, University of Delaware and Panayot S. Vassilevski, Lawrence Livermore National Laboratory) A new approach in solving Stokes systems arising from distributive relaxation method , Numerical Methods for Partial Differential Equations, 27 (2011), 898--914.

   165. pdf   2011-q2div   (With Yunqing Huang, Xiangtan University) A lowest order divergence-free finite element on rectangular grids, Frontiers of Mathematics in China, 6 (2011), No 2, 253-270.

   166. pdf  2011-div-p6   Divergence-free finite elements on tetrahedral grids for $k\ge 6$, Math. Comp. 80 (2011), 669-695.

1. 167.   2010-c1   On the full $C_1$-$Q_k$ finite element spaces on rectangles and cuboids, Adv. Appl. Math. Mech., 2 (2010), 701--721.

   168.     2010-oper.pdf  (With Xuejun Xu, Chinese Academy of Science) A new divergence-free interpolation operator with applications to the Darcy-Stokes-Brinkman equations, SIAM J. Scientific Computing,32 (2010), no. 2, 855-874.

   169.   2009-b.pdf   A family of $Q_ k+1,k \times Q_ k,k+1 $ divergence-free finite elements on rectangular grids, SIAM J. Num. Anal., 47 (2009), 2090-2107.

   170.   2009-a.pdf   A family of 3D continuously differentiable finite elements on tetrahedral grids, Applied Numerical Mathematics, 59 (2009), no. 1, 219-233.

   171.   2008-ps2.pdf   On the P1 Powell-Sabin divergence-free finite element for the Stokes equations, J. Comp. Math., 26 (2008), 456-470.

   172.    2008-c.pdf   (With David Olagunju and Anand Vyas, U of Delaware) Analytical and numerical solutions for torsional flow between coaxial discs with heat transfer, SIAM J. Appl. Math., 68 (2008), 1404-1422.

   173.     2008-b.pdf    A C1-P2 finite element without nodal basis, M2AN 42 (2008), 175-192. pdf 2021-2   ERRATUM TO "A C1-P2 FINITE ELEMENT WITHOUT NODAL BASIS", ESAIM: M2AN 55 (2021) S877-S878.

1. 174.    2007-e.pdf  (With Jinshui Qin, University of Tennessee) On the selective local stabilization of the mixed Q1-P0 element, Int. J. for Numerical Methods in Fluids, 55 (2007), 1121-141.

   175.   2007-d.pdf   Numerical integration with Taylor truncations for the quadrilateral and hexahedral finite elements, Journal of Computational and Applied Mathematics. 205 (2007), 325-342.

   176.   2007-c.pdf   (With Jinshui Qin, University of Tennessee) Stability and approximability of the P1-P0 element for Stokes equations, Int. J. for Numerical Methods in Fluids, 54 (2007), 497--515.

   177. (With Robert Gilbert, University of Delaware and Y. Xu, University of Louisville), Computing porosity of cancellous bone using ultrasonic waves, Journal of Applied Functional Anal., 2 (2007), 185--195.

   178.    2007-a.pdf    (With Huo-yuan Duan, Shao-qin Gao and Roger C. E. Tan, National University of Singapore) A Generalized BPX Framework Covering the V-cycle Nonnested Multigrid Method, Math. Comp. 76 (2007), 137-152.

   179.    2005-c.pdf  (With Jinshui Qin, University of Tennessee) Stability of the finite elements 9/(4c+1) and 9/5c for stationary Stokes equations, Computers and Structures, 84 (2005), 70-77.

   180.    2005-b.pdf  (With David Olagunju, U of Delaware) Axisymmetric Finite Element Solution of Non-isothermal Parallel-plate Flow, Applied Mathematics and Computation, 171 (2005), 1081-1094 .

   181.   2005-a.pdf   A new family of stable mixed finite elements for the 3D stokes equations, Math. Comp. 74 (2005), 543-554.

   182.    2004-a.pdf  On the nested refinement of quadrilateral and hexahedral finite elements and the affine approximation, Numer. Math. 98 (2004), 559-579.

   183. pdf 1997  1997-a.pdf  (With Zhimin Zhang, Texas Technology University) Treatments of discontinuity and bubble functions in multigrid methods, Math. Comp. 66 (1997), 1055-1072.

1. 184.    1996-b.pdf  (With Zhimin Zhang, Texas Technology University) Derivative superconvergence of rectangular finite elements for the Reissner-Mindlin plate, Comput. Methods Appl. Mech. Engrg. 134 (1996), 1-16.

   185.   1995-c.pdf    (With Peter Monk, University of Delaware) Multigrid computation of vector potentials, J. Comp. Appl. Math. , 62 (1995), 301--320.

   186.    1995-b.pdf  Successive subdivisions of tetrahedra and multigrid methods on tetrahedral meshes, Houston J. of Math. 21 (1995), 541--556.

   187.  1995-a.pdf   Optimal order non-nested multigrid methods for solving finite element equations III: On degenerate meshes, Math. Comp. 64 (1995), 23--49.

   188.   1994-d.pdf   (With Soren Jensen, University of Maryland at Baltimore County) The $p$ and $h-p$ versions of some finite element methods for Stokes problem, Comput. Methods Appl. Mech. Engrg. 116 (1994), 147--155.

   189. pdf   1994-c  (With Babak Bagheri and L. Ridgway Scott, University of Houston) Implementating and using high-order finite element methods, Finite Elements in Analysis and Design, 16 (1994), 179--189.

   190. pdf   1994-b  (With George C. Hsiao, University of Delaware) Optimal order multigrid methods for solving exterior boundary value problems, SIAM J. Numer. Anal. 31 (1994), 680--694.

   191. pdf   1994a   (With Zhimin Zhang, Texas Technology University) Wilson's element for the Reissner-Mindlin plate, Comput. Methods Appl. Mech. Engrg. 113 (1994), 55--65.

   192. pdf  1992a  (With L. Ridgway Scott, University of Houston) Higher-dimensional nonnested multigrid methods, Math. Comp. 58 (1992), 457--466.

   193. pdf   1991-a  On the convergence of spectral multigrid methods for periodic problems, Calcolo 28 (1991), 185--203.

   194. pdf  1990-c  Optimal order non-nested multigrid methods for solving finite element equations II: On non-quasiuniform meshes, Math. Comp. 55 (1990), 439--450.

   195. pdf  1990-b   Optimal order non-nested multigrid methods for solving finite element equations I: On quasiuniform meshes, Math. Comp. 55 (1990), 23--36.

   196. pdf  1990-a   (With L. Ridgway Scott, University of Houston) Finite-element interpolation of non-smooth functions satisfying boundary conditions, Math. Comp. 54 (1990), 483--493.

   197. pdf  1989   An optimal order multigrid method for biharmonic, $C^1$ finite-element equations, Numer. Math. 56 (1989), 613--624. 

Proceedings/Book Chapters

1. 198.  pdf 2021-37 Sorokina, Tatyana; Zhang, Shangyou Trivariate interpolated Galerkin finite elements for the Poisson equation. Approximation theory XVI, 237–249, Springer Proc. Math. Stat., 336, Springer, Cham, [2021], ©2021. 

   199. pdf   2013-b   (With Jianguo Huang, Shanghai Jiao Tong University and Xuehai Huang, Wenzhou University) A superconvergence of the Morley element via postprocessing, Recent advances in scientific computing and applications, 189--196, Contemp. Math., 586, Amer. Math. Soc., Providence, RI, 2013.

   200. pdf  2008-a   Some divergence-free finite elements for the stationary Stokes equations, in Advances in Mathematics and Its Applications, ed. Yanyan Li, Chi-Wang Shu, Rugang Ye and Kang Zuo, the University of Science and Technology of China Press, Hefei, 2008, 261--282.

   201. (With R. Gilbert, University of Delaware, A. Wirgin, and Y. Xu), A mathematical model for evaluation of osteoporosis, Proceedings on the Acoustics of Poro-Elastic Materials, Lyon, France, 2005, 203--210, Discrete and Computational Mathematics, Nova Science, New York, 2008, 1--16.

   202. Anisotropic Nested Refinement of Tetrahedral Grids under the Hessian Metric, Proceedings of the 2005 International Conference on Scientific Computing, Ed., H. R. Arabnia, G. A. Gravvanis, CSREA Press, 236-242, 2005.

   203. pdf 1996a   (With R. Scott, University of Houston) Multilevel iterated penalty method for mixed elements, In: Domain Decomposition Methods in Sciences and Engineering, P.E. Bjorstad, M.S. Espedal and D.E. Keyes eds., Domain Decomposition Press, Bergen 1998, 133-139.

   204. pdf 2017m   On the multigrid method for 3D mixed macro-elements, Proceedings of third ICOSAHOM, Houston J. of Math. (1996), 575--581.

   205. pdf 1994air   (With George C. Hsiao and Michael D. Marcozzi, University of Delaware) An efficient computational method for the flow past an airfoil, The 7th International Conference on Domain Decomposition, Contemporary Mathematics 180, AMS, 1994, 497--502.