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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.

Keywords

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

R2 v1 2026-06-28T15:04:06.601Z