Error estimation for finite element method on meshes that contain thin elements
Numerical Analysis
2024-08-19 v2 Numerical Analysis
Abstract
In an error estimation of finite element solutions to the Poisson equation, we usually impose the shape regularity assumption on the meshes to be used. In this paper, we show that even if the shape regularity condition is violated, the standard error estimation can be obtained if "bad" elements elements that violate the shape regularity or maximum angle condition are covered virtually by simplices that satisfy the minimum angle condition. A numerical experiment illustrates the theoretical result.
Cite
@article{arxiv.2402.18860,
title = {Error estimation for finite element method on meshes that contain thin elements},
author = {Kenta Kobayashi and Takuya Tsuchiya},
journal= {arXiv preprint arXiv:2402.18860},
year = {2024}
}
Comments
to appear in Applications of Mathematics