Finite element method for singularly perturbed problems with two parameters on a Bakhvalov-type mesh in 2D
Numerical Analysis
2020-11-26 v1 Numerical Analysis
Abstract
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 construct a new interpolation by using the characteristics of layers. Besides, a more subtle analysis of the mesh scale near the exponential layer is carried out. Based on the interpolation and new analysis of the mesh scale, we prove the optimal convergence order.
Cite
@article{arxiv.2011.12718,
title = {Finite element method for singularly perturbed problems with two parameters on a Bakhvalov-type mesh in 2D},
author = {Jin Zhang and Yanhui Lv},
journal= {arXiv preprint arXiv:2011.12718},
year = {2020}
}