56 citations · 368 across the 53 of their papers we have counts for
8 papers · 1 filter
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.…
Programming of Finite Element Methods in MATLAB
Long Chen
We discuss how to implement the linear finite element method for solving the Poisson equation. We begin with the data structure to represent the triangulation and boundary conditio…