56 citations · 368 across the 53 of their papers we have counts for
45 papers · 1 filter
Edge-averaged virtual element methods for convection-diffusion and convection-dominated problems
Shuhao Cao, Long Chen, Seulip Lee
This manuscript develops edge-averaged virtual element (EAVE) methodologies to address convection-diffusion problems effectively in the convection-dominated regime. It introduces a…
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…
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…
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…
A family of immersed finite element spaces and applications to three dimensional interface problems
Long Chen, Ruchi Guo, Jun Zou
Maxwell interface problems are of great importance in many electromagnetic applications. Unfitted mesh methods are especially attractive in 3D computation as they can circumvent ge…
Immersed Virtual Element Methods for Electromagnetic Interface Problems in Three Dimensions
Shuhao Cao, Long Chen, Ruchi Guo
Finite element methods for electromagnetic problems modeled by Maxwell-type equations are highly sensitive to the conformity of approximation spaces, and non-conforming methods may…
-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…
Immersed Virtual Element Methods for Elliptic Interface Problems in Two Dimensions
Shuhao Cao, Long Chen, Ruchi Guo +1
This article presents an immersed virtual element method for solving a class of interface problems that combines the advantages of both body-fitted mesh methods and unfitted mesh m…
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…
A Virtual Finite Element Method for Two Dimensional Maxwell Interface Problems with a Background Unfitted Mesh
Shuhao Cao, Long Chen, Ruchi Guo
A virtual element method (VEM) with the first order optimal convergence order is developed for solving two-dimensional Maxwell interface problems on a special class of polygonal me…
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…
Convergence and optimality of an adaptive modified weak Galerkin finite element method
Yingying Xie, Shuhao Cao, Long Chen +1
An adaptive modified weak Galerkin method (AmWG) for an elliptic problem is studied in this paper, in addition to its convergence and optimality. The modified weak Galerkin bilinea…
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…
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
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 .…
Convergence Analysis of the Fast Subspace Descent Methods for Convex Optimization Problems
Long Chen, Xiaozhe Hu, Steven M. Wise
The full approximation storage (FAS) scheme is a widely used multigrid method for nonlinear problems. In this paper, a new framework to design and analyze FAS-like schemes for conv…
A note on the error estimate of the virtual element methods
Shuhao Cao, Long Chen, Frank Lin
This short note reports a new derivation of the optimal order of the a priori error estimates for conforming virtual element methods (VEM) on 3D polyhedral meshes based on an error…
A Minimization Method for The Double-Well Energy Functional
Qian Zhang, Long Chen, Yifeng Xu
In this paper an iterative minimization method is proposed to approximate the minimizer to the double-well energy functional arising in the phase-field theory. The method is based…
A Preconditioner based on Non-uniform Row Sampling for Linear Least Squares Problems
Long Chen, Huiwen Wu
Least squares method is one of the simplest and most popular techniques applied in data fitting, imaging processing and high dimension data analysis. The classic methods like QR an…
Anisotropic Error Estimates of The Linear Virtual Element Method on Polygonal Meshes
Shuhao Cao, Long Chen
A refined a priori error analysis of the lowest order (linear) Virtual Element Method (VEM) is developed for approximating a model two dimensional Poisson problem. A set of new geo…
Anisotropic Error Estimates of The Linear Nonconforming Virtual Element Methods
Shuhao Cao, Long Chen
A refined a priori error analysis of the lowest order (linear) nonconforming Virtual Element Method (VEM) for approximating a model Poisson problem is developed in both 2D and 3D.…