8 papers · 1 filter
Pressure-robust optimally convergent H(div) finite element method without the commuting diagram property for the steady Oseen equations
Jin Zhang, Xiaowei Liu
This work develops a convergence theory for H(div)-conforming finite element methods applied to the steady Oseen problem, focusing on cases where the exact finite element complex h…
Supercloseness of the LDG method for a two-dimensional singularly perturbed convection-diffusion problem on Bakhvalov-type mesh
Chunxiao Zhang, Jin Zhang, Wenchao Zheng
In this paper, we focus on analyzing the supercloseness property of a two-dimensional singularly perturbed convection-diffusion problem with exponential boundary layers. The local…
Uniform convergence of finite element method on Bakhvalov-type mesh for a 2-D singularly perturbed convection-diffusion problem with exponential layers
Jin Zhang, Chunxiao Zhang
On Bakhvalov-type mesh, uniform convergence analysis of finite element method for a 2-D singularly perturbed convection-diffusion problem with exponential layers is still an open p…
Uniform convergence of optimal order under a balanced norm of a local discontinuous Galerkin method on a Shishkin mesh
Jin Zhang, Wenchao Zheng
For singularly perturbed reaction-diffusion problems in 1D and 2D, we study a local discontinuous Galerkin (LDG) method on a Shishkin mesh. In these cases, the standard energy norm…
Finite element method for singularly perturbed problems with two parameters on a Bakhvalov-type mesh in 2D
Jin Zhang, Yanhui Lv
For a singularly perturbed elliptic model problem with two small parameters, we analyze finite element methods of any order on a Bakhvalov-type mesh. For convergence analysis, we c…
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…