Supercloseness of the LDG method for a two-dimensional singularly perturbed convection-diffusion problem on Bakhvalov-type mesh
Numerical Analysis
2023-05-19 v1 Numerical Analysis
Abstract
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 discontinuous Galerkin (LDG) method with piecewise tensor-product polynomials of degree k is applied to Bakhvalov-type mesh. By developing special two-dimensional local Gauss-Radau projections and establishing a novel interpolation, supercloseness of an optimal order k+1 can be achieved on Bakhvalov-type mesh. It is crucial to highlight that this supercloseness result is independent of the singular perturbation parameter.
Keywords
Cite
@article{arxiv.2305.10778,
title = {Supercloseness of the LDG method for a two-dimensional singularly perturbed convection-diffusion problem on Bakhvalov-type mesh},
author = {Chunxiao Zhang and Jin Zhang and Wenchao Zheng},
journal= {arXiv preprint arXiv:2305.10778},
year = {2023}
}
Comments
19 pages and 1 figure