Treatments of discontinuity and bubble functions in the multigrid method. - Shangyou Zhang; Zhimin Zhang (Math. Comput., 1997)

On the nested refinement of quadrilateral and hexahedral finite elements and the affine approximation. - Shangyou Zhang (Numerische Mathematik, 2004)

Anisotropic Nested Refinement of Tetrahedral Grids Under the Hessian Metric. - Shangyou Zhang (CSC, 2005)

Axisymmetric finite element solution of non-isothermal parallel-plate flow. - Shangyou Zhang; David O. Olagunju (Appl. Math. Comput., 2005)

A new family of stable mixed finite elements for the 3D Stokes equations. - Shangyou Zhang (Math. Comput., 2005)

A generalized BPX multigrid framework covering nonnested V-cycle methods. - Huo-Yuan Duan; Shao-Qin Gao; Roger C. E. Tan; Shangyou Zhang (Math. Comput., 2007)

Errata to "A generalized BPX multigrid framework covering nonnested V-cycle methods". - Huo-Yuan Duan; Shao-Qin Gao; Roger C. E. Tan; Shangyou Zhang (Math. Comput., 2007)

Analytical and Numerical Solutions for Torsional Flow between Coaxial Discs with Heat Transfer. - David O. Olagunju; Anand B. Vyas; Shangyou Zhang (SIAM J. Appl. Math., 2008)

A Family of Qk+1, k˟Qk, k+1 Divergence-Free Finite Elements on Rectangular Grids. - Shangyou Zhang (SIAM J. Numer. Anal., 2009)

A New Divergence-Free Interpolation Operator with Applications to the Darcy–Stokes–Brinkman Equations. - Xuejun Xu; Shangyou Zhang (SIAM J. Sci. Comput., 2010)

Divergence-free finite elements on tetrahedral grids for k≥6. - Shangyou Zhang (Math. Comput., 2011)

The Lowest Order Differentiable Finite Element on Rectangular Grids. - Jun Hu 013; Yunqing Huang; Shangyou Zhang (SIAM J. Numer. Anal., 2011)

Solving Negative Order Equations by the Multigrid Method Via Variable Substitution. - George C. Hsiao; Liwei Xu; Shangyou Zhang (J. Sci. Comput., 2014)

A Simple Conforming Mixed Finite Element for Linear Elasticity on Rectangular Grids in Any Space Dimension. - Jun Hu 013; Hongying Man; Shangyou Zhang (J. Sci. Comput., 2014)

A $$C^0$$ C 0 -Weak Galerkin Finite Element Method for the Biharmonic Equation. - Lin Mu; Junping Wang; Xiu Ye; Shangyou Zhang (J. Sci. Comput., 2014)

Finite Element Formulation in Flat Coordinate Spaces to Solve Elliptic Problems on General Closed Riemannian Manifolds. - Lizhen Qin; Shangyou Zhang; Zhimin Zhang 002 (SIAM J. Sci. Comput., 2014)

A Weak Galerkin Finite Element Method for the Maxwell Equations. - Lin Mu; Junping Wang; Xiu Ye; Shangyou Zhang (J. Sci. Comput., 2015)

A Unified Mortar Condition for Nonconforming Finite Elements. - Chunmei Wang; Shangyou Zhang; Jinru Chen (J. Sci. Comput., 2015)

The minimal conforming Hk finite element spaces on Rn rectangular grids. - Jun Hu 013; Shangyou Zhang (Math. Comput., 2015)

The simplest nonconforming mixed finite element method for linear elasticity in the symmetric formulation on n-rectangular grids. - Jun Hu 013; Hongying Man; Jianye Wang; Shangyou Zhang (Comput. Math. Appl., 2016)

Stable Qk-Qk-1 mixed finite elements with discontinuous pressure. - Shangyou Zhang; Mo Mu (J. Comput. Appl. Math., 2016)

A P4 bubble enriched P3 divergence-free finite element on triangular grids. - Shangyou Zhang (Comput. Math. Appl., 2017)

A weak Galerkin least-squares finite element method for div-curl systems. - Jichun Li 001; Xiu Ye; Shangyou Zhang (J. Comput. Phys., 2018)

A Weak Galerkin Finite Element Method for Singularly Perturbed Convection-Diffusion-Reaction Problems. - Runchang Lin; Xiu Ye; Shangyou Zhang; Peng Zhu (SIAM J. Numer. Anal., 2018)

Spectral collocation methods for nonlinear coupled time fractional Nernst-Planck equations in two dimensions and its convergence analysis. - Yin Yang 003; Wanying Qiao; Jindi Wang; Shangyou Zhang (Comput. Math. Appl., 2019)

On stabilizer-free weak Galerkin finite element methods on polytopal meshes. - Xiu Ye; Shangyou Zhang (CoRR, 2019)

A conforming discontinuous Galerkin finite element method: Part II. - Xiu Ye; Shangyou Zhang (CoRR, 2019)

A conforming DG method for the biharmonic equation on polytopal meshes. - Xiu Ye; Shangyou Zhang (CoRR, 2019)

3D H2-nonconforming tetrahedral finite elements for the biharmonic equation. - Jun Hu; Shudan Tian; Shangyou Zhang (CoRR, 2019)

Stablizer-Free Weak Galerkin Methods for Monotone Quasilinear Elliptic PDEs. - Xiu Ye; Shangyou Zhang; Yunrong Zhu (CoRR, 2019)

A discontinuous least-squares finite-element method for second-order elliptic equations. - Xiu Ye; Shangyou Zhang (Int. J. Comput. Math., 2019)

A family of optimal Lagrange elements for Maxwell's equations. - Huo-Yuan Duan; Wei Liu 082; Junhua Ma; Roger C. E. Tan; Shangyou Zhang (J. Comput. Appl. Math., 2019)

Continuous mixed finite elements for the second order elliptic equation with a low order term. - Yunqing Huang; Jichun Li 001; Shangyou Zhang (J. Comput. Appl. Math., 2019)

A weak Galerkin finite element scheme for the Cahn-Hilliard equation. - Junping Wang; Qilong Zhai; Ran Zhang 002; Shangyou Zhang (Math. Comput., 2019)

New Mixed Elements for Maxwell Equations. - Huo-Yuan Duan; Zhijie Du; Wei Liu 082; Shangyou Zhang (SIAM J. Numer. Anal., 2019)

On the 2pth-Order of Convergence of the Galerkin Difference Method. - Jun Hu; Shangyou Zhang; Zhimin Zhang 002 (SIAM J. Numer. Anal., 2019)

Convergence analysis of space-time Jacobi spectral collocation method for solving time-fractional Schrödinger equations. - Yin Yang 003; Jindi Wang; Shangyou Zhang; Emran Tohidi (Appl. Math. Comput., 2020)

A locking-free weak Galerkin finite element method for Reissner-Mindlin plate on polygonal meshes. - Xiu Ye; Shangyou Zhang; Zhimin Zhang 002 (Comput. Math. Appl., 2020)

A stabilizer free weak Galerkin element method with supercloseness of order two. - Ahmed Al-Taweel; Xiaoshen Wang; Xiu Ye; Shangyou Zhang (CoRR, 2020)

Numerical investigation on weak Galerkin finite elements. - Xiu Ye; Shangyou Zhang (CoRR, 2020)

A new weak gradient for the stabilizer free weak Galerkin method with polynomial reduction. - Xiu Ye; Shangyou Zhang (CoRR, 2020)

A conforming discontinuous Galerkin finite element method for the Stokes problem on polytopal meshes. - Xiu Ye; Shangyou Zhang (CoRR, 2020)

A mixed finite element method on polytopal mesh. - Yanping Lin; Xiu Ye; Shangyou Zhang (CoRR, 2020)

A stabilizer free WG Method for the Stokes Equations with order two superconvergence on polytopal mesh. - Xiu Ye; Shangyou Zhang (CoRR, 2020)

A Pk+2 polynomial lifting operator on polygons and polyhedrons. - Xiu Ye; Shangyou Zhang (CoRR, 2020)

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

A new P1 weak Galerkin method for the Biharmonic equation. - Xiu Ye; Shangyou Zhang; Zhimin Zhang 002 (J. Comput. Appl. Math., 2020)

A discontinuous Galerkin least-squares method for div-curl systems. - Xiu Ye; Shangyou Zhang; Peng Zhu (J. Comput. Appl. Math., 2020)

A symmetric weak Galerkin method for solving non-divergence form elliptic equations. - Qilong Zhai; Tian Tian; Ran Zhang 002; Shangyou Zhang (J. Comput. Appl. Math., 2020)

The weak Galerkin finite element method for the symmetric hyperbolic systems. - Tie Zhang 002; Shangyou Zhang (J. Comput. Appl. Math., 2020)

The weak Galerkin finite element method for the transport-reaction equation. - Tie Zhang 002; Shangyou Zhang (J. Comput. Phys., 2020)

On the Uniform Convergence of the Weak Galerkin Finite Element Method for a Singularly-Perturbed Biharmonic Equation. - Ming Cui; Shangyou Zhang (J. Sci. Comput., 2020)

A Stabilizer Free Weak Galerkin Method for the Biharmonic Equation on Polytopal Meshes. - Xiu Ye; Shangyou Zhang (SIAM J. Numer. Anal., 2020)

A stabilizer-free pressure-robust finite element method for the Stokes equations. - Xiu Ye; Shangyou Zhang (Adv. Comput. Math., 2021)

A Pk+2 polynomial lifting operator on polygons and polyhedrons. - Xiu Ye; Shangyou Zhang (Appl. Math. Lett., 2021)

A weak Galerkin-mixed finite element method for the Stokes-Darcy problem. - Hui Peng; Qilong Zhai; Ran Zhang 002; Shangyou Zhang (CoRR, 2021)

de Rham complexes for weak Galerkin finite element spaces. - Chunmei Wang; Junping Wang; Xiu Ye; Shangyou Zhang (J. Comput. Appl. Math., 2021)

A stabilizer free weak Galerkin finite element method on polytopal mesh: Part II. - Xiu Ye; Shangyou Zhang (J. Comput. Appl. Math., 2021)

A stabilizer free weak Galerkin finite element method on polytopal mesh: Part III. - Xiu Ye; Shangyou Zhang (J. Comput. Appl. Math., 2021)

Development of Pressure-Robust Discontinuous Galerkin Finite Element Methods for the Stokes Problem. - Lin Mu; Xiu Ye; Shangyou Zhang (J. Sci. Comput., 2021)

Weak Galerkin finite element methods with or without stabilizers. - Xiaoshen Wang; Xiu Ye; Shangyou Zhang (Numer. Algorithms, 2021)

A Stabilizer-Free, Pressure-Robust, and Superconvergence Weak Galerkin Finite Element Method for the Stokes Equations on Polytopal Mesh. - Lin Mu; Xiu Ye; Shangyou Zhang (SIAM J. Sci. Comput., 2021)

The nodal basis of Cm-Pk3 and Cm-Pk4 finite elements on tetrahedral and 4D simplicial grids. - Shangyou Zhang (CoRR, 2022)

A parallel iterative procedure for weak Galerkin methods for second order elliptic problems. - Chunmei Wang; Junping Wang; Shangyou Zhang (CoRR, 2022)

A weak Galerkin least squares finite element method of Cauchy problem for Poisson equation. - Xiaoshen Wang; Xiu Ye; Shangyou Zhang; Peng Zhu (J. Comput. Appl. Math., 2022)

Development of a LDG method on polytopal mesh with optimal order of convergence. - Xiu Ye; Shangyou Zhang; Peng Zhu (J. Comput. Appl. Math., 2022)

An explicit weak Galerkin method for solving the first order hyperbolic systems. - Tie Zhang 002; Shangyou Zhang (J. Comput. Appl. Math., 2022)

A C0-conforming DG finite element method for biharmonic equations on triangle/tetrahedron. - Xiu Ye; Shangyou Zhang (J. Num. Math., 2022)

An Interpolated Galerkin Finite Element Method for the Poisson Equation. - Tatyana Sorokina; Shangyou Zhang (J. Sci. Comput., 2022)

On a Sharp Estimate of Overlapping Schwarz Methods in H(curl;Ω) and H(div;Ω). - Qigang Liang; Xuejun Xu; Shangyou Zhang (CoRR, 2023)

A family of stabilizer-free virtual elements on triangular meshes. - Xuejun Xu; Shangyou Zhang (CoRR, 2023)

Stabilizer-free polygonal and polyhedral virtual elements. - Yanping Lin; Mo Mu; Shangyou Zhang (CoRR, 2023)

Weak Galerkin Finite Element Methods for Optimal Control Problems Governed by Second Order Elliptic Partial Differential Equations. - Chunmei Wang; Junping Wang; Shangyou Zhang (CoRR, 2023)

Superconvergent P1 honeycomb virtual elements and lifted P3 solutions. - Yanping Lin; Xuejun Xu; Shangyou Zhang (CoRR, 2023)

A modified weak Galerkin finite element method for the linear elasticity problem in mixed form. - Xiuli Wang; Xianglong Meng; Shangyou Zhang; Huifang Zhou (J. Comput. Appl. Math., 2023)

A weak Galerkin method for elasticity interface problems. - Chunmei Wang; Shangyou Zhang (J. Comput. Appl. Math., 2023)

A time-explicit weak Galerkin scheme for parabolic equations on polytopal partitions. - Junping Wang; Xiu Ye; Shangyou Zhang (J. Num. Math., 2023)

Weak Galerkin finite element methods for quad-curl problems. - Chunmei Wang; Junping Wang; Shangyou Zhang (J. Comput. Appl. Math., 2023)

A subspace of linear nonconforming finite element for nearly incompressible elasticity and Stokes flow. - Shangyou Zhang (J. Num. Math., 2023)

An H-div finite element method for the Stokes equations on polytopal meshes. - Xiu Ye; Shangyou Zhang (Comput. Appl. Math., 2024)

New Analysis of Overlapping Schwarz Methods for Vector Field Problems in Three Dimensions with Generally Shaped Domains. - Duk-Soon Oh; Shangyou Zhang (CoRR, 2024)

Convergent finite elements on arbitrary meshes, the WG method. - Ran Zhang 002; Shangyou Zhang (CoRR, 2024)

A nonconforming P3 and discontinuous P2 mixed finite element on tetrahedral grids. - Xuejun Xu; Shangyou Zhang (CoRR, 2024)

A nonconforming P2 and discontinuous P1 mixed finite element on tetrahedral grids. - Shangyou Zhang (CoRR, 2024)

Simplified Weak Galerkin Methods for Linear Elasticity on Nonconvex Domains. - Chunmei Wang; Shangyou Zhang (CoRR, 2024)

Weak Galerkin methods for elliptic interface problems on curved polygonal partitions. - Dan Li; Chunmei Wang; Shangyou Zhang (J. Comput. Appl. Math., 2024)

Weak Galerkin finite element methods for optimal control problems governed by second order elliptic equations. - Chunmei Wang; Junping Wang; Shangyou Zhang (J. Comput. Appl. Math., 2024)

A modified weak Galerkin finite element method for the Maxwell equations on polyhedral meshes. - Chunmei Wang; Xiu Ye; Shangyou Zhang (J. Comput. Appl. Math., 2024)

Low regularity error analysis for an H(div)-conforming discontinuous Galerkin approximation of Stokes problem. - Yuping Zeng; Liuqiang Zhong; Feng Wang; Mingchao Cai; Shangyou Zhang (J. Comput. Appl. Math., 2024)

A pressure-robust numerical scheme for the Stokes equations based on the WOPSIP DG approach. - Yuping Zeng; Liuqiang Zhong; Feng Wang; Shangyou Zhang; Mingchao Cai (J. Comput. Appl. Math., 2024)

Corrigendum to "A pressure-robust numerical scheme for the Stokes equations based on the WOPSIP DG approach" [Journal of Computational and Applied Mathematics 445 (2024) 115819]. - Yuping Zeng; Liuqiang Zhong; Feng Wang; Shangyou Zhang; Mingchao Cai (J. Comput. Appl. Math., 2024)

Order two superconvergence of the CDG finite elements for non-self adjoint and indefinite elliptic equations. - Xiu Ye; Shangyou Zhang (Adv. Comput. Math., 2024)

Four-order superconvergent CDG finite elements for the biharmonic equation on triangular meshes. - Xiu Ye; Shangyou Zhang (J. Comput. Appl. Math., 2024)

A Modified Rotated-Q1 Finite Element for the Stokes Equations on Quadrilateral and Hexahedral Meshes. - Liwei Xu; Xuejun Xu; Shangyou Zhang (J. Sci. Comput., 2024)

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

Conforming and Nonconforming Virtual Element Methods for Signorini Problems. - Yuping Zeng; Liuqiang Zhong; Mingchao Cai; Feng Wang; Shangyou Zhang (J. Sci. Comput., 2024)

On an accurate numerical integration for the triangular and tetrahedral spectral finite elements. - Ziqing Xie; Shangyou Zhang (Adv. Comput. Math., 2024)

A 𝐶1-𝑃7 Bell Finite Element on Triangle. - Xuejun Xu; Shangyou Zhang (Comput. Methods Appl. Math., 2024)

Three Low Order H-Curl-Curl Finite Elements on Triangular Meshes. - Shangyou Zhang (Comput. Methods Appl. Math., 2024)

Efficient weak Galerkin finite element methods for Maxwell equations on polyhedral meshes without convexity constraints. - Chunmei Wang; Shangyou Zhang (J. Comput. Appl. Math., 2025)

Auto-stabilized weak Galerkin finite element methods for Stokes equations on non-convex polytopal meshes. - Chunmei Wang; Shangyou Zhang (J. Comput. Phys., 2025)

A nonsingular-kernel Dirichlet-to-Dirichlet mapping method for the exterior Stokes problem. - Xiaojuan Liu; Maojun Li; Tao Yin; Shangyou Zhang (Adv. Comput. Math., 2025)

Stabilizer-free Weak Galerkin Methods for Quad-Curl Problems on polyhedral Meshes without Convexity Assumptions. - Chunmei Wang; Shangyou Zhang (CoRR, 2025)

A Simple Weak Galerkin Finite Element Method for a Class of Fourth-Order Problems in Fluorescence Tomography. - Chunmei Wang; Shangyou Zhang (CoRR, 2025)

Locking-Free HDG Methods for Reissner-Mindlin Plates Equations on Polygonal Meshes. - Gang Chen 025; Lu Zhang 029; Shangyou Zhang (J. Sci. Comput., 2025)

A P 2 H-Div-Nonconforming-H-Curl Finite Element for the Stokes Equations on Triangular Meshes. - Yunqing Huang; Xuejun Xu; Shangyou Zhang (Comput. Methods Appl. Math., 2025)

Two families of C1-Pk Fraeijs de Veubeke-Sander finite elements on quadrilateral meshes. - Shangyou Zhang (CoRR, 2025)

Superconvergent quadriatic finite element on uniform tetrahedral meshes. - Yunqing Huang; Shangyou Zhang (CoRR, 2025)

A nodal basis for the C1-P33 finite elements on 5D simplex grids. - Jun Hu; Shangyou Zhang (CoRR, 2025)

Rectangular C1-Qk Bell finite elements in two and three dimensions. - Hongling Hu; Shangyou Zhang (CoRR, 2025)

Stabilizing the Scott-Vogelius elements by Guzman-Neilan bubble functions on triangular meshes. - Shangyou Zhang (J. Appl. Math. Comput., 2025)

Three families of C1-P2m+1 Bell finite elements on triangular meshes. - Xuejun Xu; Shangyou Zhang (Numer. Algorithms, 2025)

A family of P4 macro-bubble enriched C1-Pk finite elements on triangular meshes. - Shangyou Zhang (Numerische Mathematik, 2025)

Weak Galerkin Methods for the Brinkman Equations. - Chunmei Wang; Shangyou Zhang (CoRR, 2025)

A Simple and Robust Weak Galerkin Method for the Brinkman Equations on Non-Convex Polytopal Meshes. - Chunmei Wang; Shangyou Zhang (CoRR, 2025)

A nonconforming P3+B4 and discontinuous P2 mixed finite element on tetrahedral grids. - Xuejun Xu; Shangyou Zhang (Adv. Comput. Math., 2025)

A medius error analysis for the conforming discontinuous Galerkin finite element methods. - Yuping Zeng; Shangyou Zhang (J. Num. Math., 2025)

An auto-stabilized weak Galerkin method for elasticity interface problems on nonconvex meshes. - Chunmei Wang; Shangyou Zhang (J. Comput. Appl. Math., 2026)