Shangyou Zhang

Teaching (Spring 2025):

1.  MATH 426 010 12:40PM - 1:35PM  MWF, Feb 3 - May 15   MEM108

Recent publication:    ( All publications  )

1. 2025-c1pk  A family of P4 macro-bubble enriched C1-Pk finite elements on triangular meshes 

2. 2025-s-e On the Superconvergence of a Conforming Mixed Finite Element for Linear Elasticity on Uniform n-Square Grids 

3. 2025-iP  Interpolated Galerkin finite elements on rectangular and cuboid meshes for the Poisson equation 

4. 2025-md A Potential-Robust WG Finite Element Method for the Maxwell Equations on Tetrahedral Meshes

5. 2025-rm   Locking-Free HDG Methods for Reissner–Mindlin Plates Equations on Polygonal Meshes 

6. 2025-ngb   Stabilizing the Scott-Vogelius elements by Guzman-Neilan bubble functions on triangular meshes

7.  2024-he Two-Order Superconvergent CDG Finite Element Method for the Heat Equation on Triangular and Tetrahedral Meshes

8. 2025-ife Interpolated Galerkin finite elements on rectangular and cuboid meshes for the biharmonic equation, 

  Shown on MATH REVIEWS (5/11/2025) : 

1. 1.  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.

   2. 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.

   3. 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. 

   4. 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.  

   5.  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. 

   6.  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.

   7. 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.

   8.  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. 

   9.  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.

   10. 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. 

   11. 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.

   12.  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.

   13. 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.

   14. 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. 

   15. 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. 16.  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. 

   17. 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. 

   18. 2024-c1p    Xu, Xuejun; Zhang, Shangyou; A C1-P7 Bell Finite Element on Triangle. Comput. Methods Appl. Math. 24 (2024), no. 4, 995–1000.

   19. 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.

   20. 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.

   21. 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. 

   22. 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.

   23. 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.  

   24. 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.

   25. 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.

   26. 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.

   27. 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.

   28. 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.

   29.  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.

   30.  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.

   31.  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.

   32. 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.

   33. 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. 

   34. 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. 

   35.  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.

   36.  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.  

   37.  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. 

   38.  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. 

   39.  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. 

   40.  2024-hd    Zhang, Shangyou; Zhu, Peng BDM H(div) weak Galerkin finite element methods for Stokes equations. Appl. Numer. Math. 197 (2024), 307–321. 

   41.   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. 

 All publications 

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