7 papers
Semi-robust equal-order hybridized discontinuous methods
Xiaoqi Ma, Jin Zhang
This paper introduces a unified analysis framework of equal-order hybridized discontinuous finite element (HDG) methods. The general framework covers standard HDG, embedded discont…
Supercloseness of the HDG method on Shishkin mesh for a singularly perturbed convection diffusion problem in 2D
Xiaoqi Ma, Jin Zhang
This paper presents the first analysis of parameter-uniform convergence for a hybridizable discontinuous Galerkin (HDG) method applied to a singularly perturbed convection-diffusio…
Supercloseness of the DDG method for a singularly perturbed convection diffusion problem on Shishkin mesh
Xiaoqi Ma, Jin Zhang, Xinyi Feng +1
This paper investigates the supercloseness of a singularly perturbed convection diffusion problem using the direct discontinuous Galerkin (DDG) method on a Shishkin mesh. The main…
Uniform convergence of optimal order of a local discontinuous Galerkin method on a Shishkin mesh under a balanced norm
Xiaoqi Ma, Jin Zhang, Wenchao Zheng
This article investigates a local discontinuous Galerkin (LDG) method for one-dimensional and two-dimensional singularly perturbed reaction-diffusion problems on a Shishkin mesh. D…
Supercloseness of the NIPG method for a singularly perturbed convection diffusion problem on Shishkin mesh in 2D
Xiaoqi Ma, Jin Zhang
As a popular stabilization technique, the nonsymmetric interior penalty Galerkin (NIPG) method has significant application value in computational fluid dynamics. In this paper, we…
Supercloseness analysis of the nonsymmetric interior penalty Galerkin method on Bakhvalov-type mesh
Xiaoqi Ma, Jin Zhang
In this paper, we study the convergence of the nonsymmetric interior penalty Galerkin (NIPG) method on a Bakhvalov-type mesh for the first time. For this purpose, a new composite i…
Supercloseness of the NIPG method for a singularly perturbed convection diffusion problem on Shishkin mesh
Jin Zhang, Xiaoqi Ma
In this paper, we analyze the supercloseness result of nonsymmetric interior penalty Galerkin (NIPG) method on Shishkin mesh for a singularly perturbed convection diffusion problem…