D. Green, X. Hu, Jeremy Lore, L. Mu, M.L. Stowell, An Efficient High-order Numerical Solver for Diffusion Equations with Strong Anisotropy, Computer Physics Communications, 276 (2022), 108333, doi.org/10.1016/j.cpc.2022.108333.

L. Mu, A Pressure-Robust Weak Galerkin Finite Element Method for Navier-Stokes Equations, Numerical Methods for Partial Differential Equations 39 (3), 2327-2354.

G. Zhang and L. Mu, A non-intrusive domain-decomposition model reduction method for linear steady-state PDEs with random coefficients, Numerical Partial Differential Equation. 2021,  https://doi.org/10.1002/num.22856.

L. Mu, X. Ye, and S. Zhang, Development of pressure-robust discontinuous Galerkin finite element methods for the Stokes problem, Journal of Scientific Computing, 89 (2021).  

L. Mu, X. Ye, and S. Zhang, A Stabilizer Free, Pressure Robust, and Superconvergence Weak Galerkin Finite Element Method for the Stokes Equations on Polytopal Mesh, SIAM Journal on Scientific Computing, 43(4), A2614–A2637.

L. Liu, Z. Chen, and L. Mu, Solving the Linear Transport Equation by a Deep Neural Network Approach, Discrete and Continuous Dynamical Systems, doi: 10.3934/dcdss.2021070.

G. Wang, L. Mu, Y. Wang, and Y. He, A Pressure-robust Virtual Element Method for the Stokes Problem, Computer Methods in Applied Mechanics and Engineering, 382(2021) 113879. 

C. He, W. Hu, and L. Mu, Optimal Control of Convection-Cooling and Numerical Implementation, Computers & Mathematics with Applications, 92 (2021): 48-61. 

Ahmed AL-Taweel, L. Mu, A New Upwind Weak Galerkin Finite Element Method for Linear Hyperbolic Equations,  Journal of Computational and Applied Mathematics, 390 (2021): 113376. 

 D.  Demidov, L. Mu, and B.  Wang, Accelerating linear solvers for large-scale Stokes problems with C++ metaprogramming, Journal of Computational Science, 49 (2021): 101285. 

L. Mu and Z. Chen, A New WENO Weak Galerkin Finite Element Method for Time Dependent Hyperbolic Equations, Applied Numerical Mathematics, 159 (2021): 106-124. 

B. Wang and L. Mu, Viscosity robust weak Galerkin finite element methods for Stokes problem, Electronic Research Archive, 29 (2021): 1881-1895. 

L. Mu. Weak Galerkin Finite Element with Curved Edges. Journal of Computational and Applied Mathematics. 381 (2021): 113038.

E. D’Azevedo, D. Green, L. Mu. Discontinuous Galerkin Sparse Grids Methods for Time Domain Maxwell’s Equations. Computer Physics Communications. 256 (2020): 107412.

L. Mu. A Uniformly Robust H(div) Weak Galerkin Finite Element Methods for Brinkman Problems. SIAM Journal on Numerical Analysis, 58 (2020), 1422–1439. 

L. Mu. Pressure Robust Weak Galerkin Finite Element Methods for Stokes Problems. SIAM Journal on Scientific Computing, 42 (2020), B608–B629. 

F. Bao, L. Mu, and J. Wang. A Fully Computable A Posteriori Error Estimate for the Stokes Equations on Polytopal Meshes. SIAM Journal on Numerical Analysis, 57 (2019), 458-477. 

L. Mu. Weak Galerkin Based A Posteriori Error Estimates for Second Order Elliptic Interface Problems on Polygonal Meshes. Journal of Computational and Applied Mathematics, 361 (2019): 413-425. 

L. Mu, X. Ye, and S. Zhang. Development of A P2 Element with Optimal L2 Convergence for Biharmonic Equation. Numerical Methods for Partial Differential Equations, 35 (2019): 1497-1508. 

L. Mu. A Priori and A Posteriori Error Estimates for Elliptic Interface Problems for A New Weak Galerkin Finite Element Methods. Journal of Computational and Applied Mathematics, 362 (2019): 423-442.

L. Mu, X. Zhang. An Immersed Weak Galerkin Method For Elliptic Interface Problems. Journal of Computational and Applied Mathematics, 362 (2019): 471-483. 

H. Li, L. Mu, Xiu Ye. A Posteriori Error Estimator for Weak Galerkin Finite Element Method on Polytopal Mesh. Communications in Computational Physics, 26 (2019): 558-578. 

X. Hu, L. Mu, X. Ye. A Weak Galerkin Finite Element Method for the Navier-Stokes Equations. Journal of Computational and Applied Mathematics, 362 (2019): 614-625. 

R. Huang, L. Mu. A New Fast Method of Solving the High Dimensional Elliptic Eigenvalue Problem. Applied Mathematics and Computation, 356 (2019): 338-346. 

R. Wang, L. Mu, X. Ye. A Locking Free Reissner-Mindlin Element with Weak Galerkin Rotations. Discrete and Continuous Dynamical Systems -B, 24 (2019): 351-361. 

J. Adler, X. Hu, L. Mu, X. Ye. An a Posteriori Error Estimator for the Weak Galerkin Least-Squares Finite-Element Method. Journal of Computational and Applied Mathematics. 362 (2019): 383-399. 

Z. Cang, L. Mu, and G. Wei. Representability of Algebraic Topology for Biomolecules in Machine Learning Based Scoring and Virtual Screening. PLOS Computational Biology, 14 (2018): e1005929. 

L. Mu, G. Zhang. A Domain-decomposition-based Sparse Approximation for Convection-diffusion Equations with Random Coefficients. SIAM J. Sci. Comput., 41 (2018), A1984–A2011. 

H. Li, L. Mu, X. Ye. Interior Energy Estimates for the Weak Galerkin Finite Element Method. Numerische Mathematik, 139 (2018): 447-478. 

K. Xia, Z. Li and L. Mu. Multiscale Persistent Functions for Biomolecular Structure Characterization. Bulletin of Mathematical Biology, 80 (2018): 1-31. 

L. Mu, J. Wang, X. Ye, and S. Zhang. A Discrete Divergence Free Weak Galerkin Finite Element Method for the Stokes Equations. Applied Numerical Mathematics, 125 (2018):172-182. 

L. Mu, J. Wang, and X. Ye. A Weak Galerkin Method for the Reissner-Mindlin Plate in Primary Form. Journal of Scientific Computing, 75 (2018): 782-802. 

X. Hu, L. Mu, X. Ye. Weak Galerkin Method for the Biot’s Consolidation Model. Computers and Mathematics with Applications, 75 (2018): 2017-2030. 

L. Mu, and X. Ye. A Simple Finite Element Method for Linear Hyperbolic Equation. Journal of Computational and Applied Mathematics, 330 (2018): 330-339. 

Z. Chen, L. Liu, L. Mu. DG-IMEX Stochastic Galerkin Schemes for Linear Transport Equation with Random Inputs and Diffusive Scalings. Journal of Scientific Computing, 73 (2017): 566-592. 

L. Mu, K. Xia, and G. Wei. Geometric and Electrostatic Modeling Using Molecular Rigidity Functions. Journal of Computational and Applied Mathematics, 313 (2017): 18-37. 

L. Mu, J. Wang, and X. Ye. A Least-squares Based Weak Galerkin Finite Element Method for Second Order Elliptic Equations, SIAM J. Sci. Comput., 39(2017): A1531-A1557. 

X. Hu, L. Mu, X. Ye. A Simple Finite Element Method of the Cauchy Problem for Poisson Equation. International Journal of Numerical Analysis and Modeling, 14 (2017), N4-5, 591-603. 

L. Mu, J. Wang, and X. Ye. Effective Implementation of the Weak Galerkin Finite Element Methods for the Biharmonic Equation. Computers & Mathematics with Applications, 74 (2017): 1215-1222. 

L. Mu, X. Ye. A Simple Finite Element Method for the Stokes Equations. Advances in Computational Mathematics, 43 (2017): 1305-1324. 

L. Mu, X. Ye. A Simple Finite Element Method for Non-divergence form Elliptic Equations. Interna- tional journal of Numerical Analysis and Modeling, 14 (2017): 306-311. 

L. Mu, J. Wang, and X. Ye. A weak Galerkin Generalized Multiscale Finite Element Method. Journal of Computational and Applied Mathematics, 305 (2016): 68-81. 

L. Mu, J. Wang, X. Ye, and S. Zhao. A new weak Galerkin finite element method for elliptic interface problems. Journal of Computational Physics, 325 (2016): 157-173. 

L. Mu, J. Wang, and X. Ye. A Hybridized Formulation for the Weak Galerkin Mixed Finite Element Method. Journal of Computational and Applied Mathematics, 307(2016): 335-345. 

Q. Zhai, R. Zhang, L. Mu. A New Weak Galerkin Finite Element Scheme for the Brinkman Model. Communications in Computational Physics, 19 (2016): 1409-1434. 

T. Zhang, L. Mu, J. Yuan. A Posteriori Error Estimates of Stabilized Finite Volume Method for the Stokes Equations. Mathematical Methods in the Applied Sciences, 39 (2016): 32-43 

L. Mu, X. Wang, and Y. Wang. Shape Regularity Conditions for Polygonal/polyhedral Meshes, Exemplified in a Discontinuous Galerkin Discretization. Numerical Methods for Partial Differential Equations, 31 (2015): 308-325. 

L. Mu, J. Wang, and X. Ye. A Weak Galerkin Finite Element Method with Polynomial Reduction. Journal of Computational and Applied Mathematics, 285 (2015): 45-58. 

L. Mu, J. Wang, X. Ye, and S. Zhang. A Weak Galerkin Finite Element Method for the Maxwell Equations. Journal of Scientific Computing, 65 (2015): 363-386. 

F. Gao, X. Wang, L. Mu. A Modified Weak Galerkin Finite Element Methods for Convection-diffusion Problems in 2D. Journal of Applied Mathematics and Computing, 49 (2015): 493-511. 

L. Mu, J. Wang, and X. Ye. Weak Galerkin Finite Element Methods on Polytopal Meshes. International Journal of Numerical Analysis and Modeling, 12 (2015), 31-53. 

L. Mu, X. Wang, and X. Ye. A Modified Weak Galerkin Finite Element Method for the Stokes Equations. Journal of Computational and Applied Mathematics, 275 (2015): 79-90. 

L. Mu, J. Wang, and X. Ye. A New Weak Galerkin Finite Element Method for the Helmholtz Equation. IMA Journal of Numerical Analysis, 35 (2015): 1228-1255. 

R. Jari, L. Mu. Superconvergence of H(div) Finite Element Approximations for the Stokes Problem by Local L2-projection Methods. Journal of Computational and Applied Mathematics, 278 (2015): 278-292. 

Z. Cang, L. Mu, K. Wu, K. Opron, K. Xia, G. Wei. A Topological Approach for Protein Classification. Molecular Based Mathematical Biology, 3 (2015): 140-162. 

L. Mu and R. Jari. A Posteriori Error Analysis for Discontinuous Finite Volume Methods of Elliptic Interface Problems. Journal of Computational and Applied Mathematics, 255 (2014): 529-543. 

G. Lin, J. Liu, L. Mu, and X. Ye. Weak Galerkin Finite Element Methods for Darcy Flow: Anisotropy and Heterogeneity. Journal of Computational Physics, 276 (2014) 422-437. 

L. Mu, J. Wang, and X. Ye. A Stable Numerical Algorithm for the Brinkman Equations by Weak Galerkin Finite Element Methods. Journal of Computational Physics, 273 (2014): 327-342. 

L. Mu, J. Wang, X. Ye, and S. Zhao. Numerical Studies on the Weak Galerkin Method for the Helmholtz Equation with Large Wave Number. Communications in Computational Physics, 15 (2014): 1461-1479. 

L. Mu, J. Wang, and X. Ye. Weak Galerkin Finite Element Methods for the Biharmonic Equation on Polytopal Meshes. Numerical Methods for Partial Differential Equations, 30 (2014): 1003-1029. 

L. Mu, J. Wang, X. Ye, and S. Zhang. A C0-Weak Galerkin Finite Element Methods for the Biharmonic Equation. Journal of Scientific Computing, 59 (2014): 473-495. 

L. Mu, J. Wang, Y. Wang, and X. Ye. Interior Penalty Discontinuous Galerkin Method on Very General Polygonal and Polyhedral Meshes. Journal of Computational and Applied Mathematics, 255 (2014): 432–440. 

F. Gao, L. Mu. On L2 Error Estimate for Weak Galerkin Finite Element Methods for Parabolic Problems. Journal of Computational Mathematics, 32 (2014): 195-204. 

L. Mu and R. Jari. A Recovery-based Error Estimate for Nonconforming Finite Volume Methods of Interface Problems. Applied Mathematics and Computation, 220 (2013): 63-74. 

L. Mu, J. Wang, Y. Wang, and X. Ye. A Weak Galerkin Mixed Finite Element Method for Biharmonic Equation. Numerical Solution of Partial Differential Equations: Theory, Algorithms, and Their Applications, 45 (2013): 247-277. 

L. Mu, J. Wang, G. Wei, X. Ye, and S. Zhao. Weak Galerkin Methods for Second Order Elliptic Interface Problems. Journal of Computational Physics, 250 (2013): 106-125. 

L. Mu, J. Wang, Y. Wang, and X. Ye. A Computational Study of the Weak Galerkin Method for Second-order Elliptic Equations. Numerical Algorithms, 63 (2013): 753-777. 

L. Mu, R. Jari, and L. Conner. A Recovery-Based Error Estimator for Finite Volume Methods of Interface Problems: Conforming Linear Element. Numerical Methods for Partial Differential Equations, 29 (2013): 131-143. 

R. Jari, L. Mu, and X. Ye. Superconvergence of H(div) Finite Element Approximations for the Stokes Problem by L2-Projection Methods. Applied Mathematics and Computation, 29 (2013): 5649-5656. 

R. Jari, L. Mu, A. Harris, and L. Fox. Superconvergence for Discontinuous Galerkin Finite Element Methods by L2-projection Methods. Computers and Mathematics with Applications, 65 (2013): 665-672. 

J. Liu, L. Mu, X. Ye. L2 Error Estimation for DGFEM for Elliptic Problems with Low Regularity. Applied Mathematics Letters, 25 (2012): 1614-1618. 

J. Liu, L. Mu, X. Ye, and R. Jari. Convergence of the Discontinuous Finite volume Method for Elliptic Problems with minimal Regularity. Journal of Computational and Applied Mathematics, 236 (2012):4537- 4546. 

J. Liu, L. Mu, X. Ye. An Adaptive Discontinuous Finite Volume Methods for Elliptic Problem. Journal of Computational and Applied Mathematics, 235 (2011): 5422-5431. 

L. Mu and X. Ye. A Finite Volume Method for Solving Navier-Stokes Problems. Nonlinear Analysis: Theory, Methods & Applications, 74 (2011): 6686-6695. 

J. Liu, L. Mu, X. Ye. A Comparative Study of Locally Conservative Numerical Methods for Darcy Flows. Procedia Computer Science, 4 (2011): 974–983. 

N. Amraji, L. Mu, M. Milanova. Shape-based Human Actions Recognition in Videos. HCII 2011, LNCS 6761, 539-546. 

C. He, X. Hu, and L. Mu, A Mesh-free Method Using Piecewise Deep Neural Network for Elliptic Interface Problems, Submitted.