12 citations · 62 across the 32 of their papers we have counts for
32 papers
A Staggered Discontinuous Galerkin Method for linear elasticity problem on Polytopal Meshes
Long Chen, Xuehai Huang, Ruishu Wang +1
This paper develops a novel staggered discontinuous Galerkin (SDG) method for linear elasticity based on the Hellinger-Reissner variational principle. We construct symmetric stress…
A robust interior penalty method for a gradient-elastic Kirchhoff plate model
Mingqing Chen, Jianguo Huang, Xuehai Huang
This paper is devoted to proposing and analyzing a robust interior penalty method for a gradient-elastic Kirchhoff plate (GEKP) model over a convex polygon. The numerical met…
Geometric Decomposition and Efficient Implementation of High Order Face and Edge Elements
Chunyu Chen, Long Chen, Xuehai Huang +1
This study investigates high-order face and edge elements in finite element methods, with a focus on their geometric attributes, indexing management, and practical application. The…
A New Div-Div-Conforming Symmetric Tensor Finite Element Space with Applications to the Biharmonic Equation
Long Chen, Xuehai Huang
A new -conforming finite element is presented, which avoids the need for super-smoothness by redistributing the degrees of freedom to edges and faces. This lead…
Virtual Element Methods Without Extrinsic Stabilization
Chunyu Chen, Xuehai Huang, Huayi Wei
Virtual element methods (VEMs) without extrinsic stabilization in arbitrary degree of polynomial are developed for second order elliptic problems, including a nonconforming VEM and…
Complexes from Complexes: Finite Element Complexes in Three Dimensions
Long Chen, Xuehai Huang
In the field of solving partial differential equations (PDEs), Hilbert complexes have become highly significant. Recent advances focus on creating new complexes using the Bernstein…
A robust lower order mixed finite element method for a strain gradient elasticity model
Mingqing Chen, Jianguo Huang, Xuehai Huang
A robust nonconforming mixed finite element method is developed for a strain gradient elasticity (SGE) model. In two and three dimensional cases, a lower order -continuous $H^…
Robust mixed finite element methods for a quad-curl singular perturbation problem
Xuehai Huang, Chao Zhang
Robust mixed finite element methods are developed for a quad-curl singular perturbation problem. Lower order H(grad curl)-nonconforming but H(curl)-conforming finite elements are c…
Finite Element de Rham and Stokes Complexes in Three Dimensions
Long Chen, Xuehai Huang
Finite element de Rham complexes and finite element Stokes complexes with various smoothness in three dimensions are systematically constructed. First smooth scalar finite elements…
Finite Element Complexes in Two Dimensions
Long Chen, Xuehai Huang
In this study, two-dimensional finite element complexes with various levels of smoothness, including the de Rham complex, the curldiv complex, the elasticity complex, and the divdi…
-conforming Finite Element Tensors with Constraints
Long Chen, Xuehai Huang
A unified construction of -conforming finite element tensors, including vector element, symmetric matrix element, traceless matrix element, and, in general, tensor…
Geometric decompositions of the simplicial lattice and smooth finite elements in arbitrary dimension
Long Chen, Xuehai Huang
Recently -conforming finite elements on simplexes in arbitrary dimension are constructed by Hu, Lin and Wu. The key in the construction is a non-overlapping decomposition of t…
A finite element elasticity complex in three dimensions
Long Chen, Xuehai Huang
A finite element elasticity complex on tetrahedral meshes is devised. The conforming finite element is the smooth finite element developed by Neilan for the velocity field in…
Finite elements for div and divdiv conforming symmetric tensors in arbitrary dimension
Long Chen, Xuehai Huang
Several div-conforming and divdiv-conforming finite elements for symmetric tensors on simplexes in arbitrary dimension are constructed in this work. The shape function space is fir…
-Conforming Virtual Elements in Arbitrary Dimension
Xuehai Huang
The -conforming virtual elements of any degree on any shape of polytope in with and are recursively constructed by gluing conforming vi…
Error analysis of a decoupled finite element method for quad-curl problems
Shuhao Cao, Long Chen, Xuehai Huang
Finite element approximation to a decoupled formulation for the quad--curl problem is studied in this paper. The difficulty of constructing elements with certain conformity to the…
Discrete Hessian complexes in three dimensions
Long Chen, Xuehai Huang
A family of conforming virtual element Hessian complexes on tetrahedral meshes are constructed based on decompositions of polynomial tensor spaces. They are applied to discretize t…
A Morley-Wang-Xu element method for a fourth order elliptic singular perturbation problem
Xuehai Huang, Yuling Shi, Wenqing Wang
A Morley-Wang-Xu (MWX) element method with a simply modified right hand side is proposed for a fourth order elliptic singular perturbation problem, in which the discrete bilinear f…
Nonconforming finite element Stokes complexes in three dimensions
Xuehai Huang
Two nonconforming finite element Stokes complexes starting from the conforming Lagrange element and ending with the nonconforming - element for the Stokes equation in thr…
Finite elements for divdiv-conforming symmetric tensors in three dimensions
Long Chen, Xuehai Huang
Two types of finite element spaces on a tetrahedron are constructed for divdiv conforming symmetric tensors in three dimensions. The key tools of the construction are the decomposi…
Piecewise Divergence-Free Nonconforming Virtual Elements for Stokes Problem in Any Dimensions
Huayi Wei, Xuehai Huang, Ao Li
Piecewise divergence-free nonconforming virtual elements are designed for Stokes problem in any dimensions. After introducing a local energy projector based on the Stokes problem a…
Finite elements for divdiv-conforming symmetric tensors
Long Chen, Xuehai Huang
Two types of finite element spaces on triangles are constructed for div-div conforming symmetric tensors. Besides the normal-normal continuity, the stress tensor is continuous at v…
Nonconforming Virtual Element Method for -th Order Partial Differential Equations in with
Xuehai Huang
The -nonconforming virtual elements of any order on any shape of polytope in with constraints and are constructed in a universal way. A gener…
Nonconforming Virtual Element Method for -th Order Partial Differential Equations in
Long Chen, Xuehai Huang
A unified construction of the -nonconforming virtual elements of any order is developed on any shape of polytope in with constraints and .…