23 citations · 27 across the 7 of their papers we have counts for
7 papers
Convergence of a finite element method on a Bakhvalov-type mesh for a singularly perturbed convection--diffusion equation in 2D
Jin Zhang, Xiaowei Liu
A finite element method of any order is applied on a Bakhvalov-type mesh to solve a singularly perturbed convection--diffusion equation in 2D, whose solution exhibits exponential b…
Convergence and supercloseness in a balanced norm of finite element methods on Bakhvalov-type meshes for reaction-diffusion problems
Jin Zhang, Xiaowei Liu
In convergence analysis of finite element methods for singularly perturbed reaction--diffusion problems, balanced norms have been successfully introduced to replace standard energy…
Optimal order of uniform convergence for finite element method on Bakhvalov-type meshes
Jin Zhang, Xiaowei Liu
We propose a new analysis of convergence for a th order () finite element method, which is applied on Bakhvalov-type meshes to a singularly perturbed two-point boundary…
Estimations of the discrete Green's function of the SDFEM on Shishkin triangular meshes for singularly perturbed problems with characteristic layers
Xiaowei Liu, Jin Zhang
In this technical report, we present estimations of the discrete Green's function of the streamline diffusion finite element method (SDFEM) on Shishkin triangular meshes for singul…
Supercloseness of the SDFEM on Shishkin triangular meshes for problems with exponential layers
Jin Zhang, Xiaowei Liu
In this paper, we analyze the supercloseness property of the streamline diffusion finite element method (SDFEM) on Shishkin triangular meshes, which is different from one in the ca…
Analysis of the SDFEM in a modified streamline diffusion norm for singularly perturbed convection diffusion problems
Jin Zhang, Xiaowei Liu
In this paper we consider a model singularly perturbed convection diffusion problem which is solved by a streamline diffusion finite element method (SDFEM) on a Shishkin rectangula…
Analysis of SDFEM on Shishkin triangular meshes and hybrid meshes for problems with characteristic layers
Jin Zhang, Xiaowei Liu
In this paper, we analyze the streamline diffusion finite element method (SDFEM) for a model singularly perturbed convection-diffusion equation on a Shishkin triangular mesh and hy…