Convergence of a finite element method on a Bakhvalov-type mesh for a singularly perturbed convection--diffusion equation in 2D
Numerical Analysis
2020-11-12 v1 Numerical Analysis
Abstract
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 boundary layers. A uniform convergence of (almost) optimal order is proved by means of a carefully defined interpolant.
Keywords
Cite
@article{arxiv.2011.05611,
title = {Convergence of a finite element method on a Bakhvalov-type mesh for a singularly perturbed convection--diffusion equation in 2D},
author = {Jin Zhang and Xiaowei Liu},
journal= {arXiv preprint arXiv:2011.05611},
year = {2020}
}