Error estimation for finite element solutions on meshes that contain thin elements

Kenta Kobayashi; Takuya Tsuchiya

Applications of Mathematics (2024)

  • Volume: 69, Issue: 5, page 571-588
  • ISSN: 0862-7940

Abstract

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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 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.

How to cite

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Kobayashi, Kenta, and Tsuchiya, Takuya. "Error estimation for finite element solutions on meshes that contain thin elements." Applications of Mathematics 69.5 (2024): 571-588. <http://eudml.org/doc/299321>.

@article{Kobayashi2024,
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 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.},
author = {Kobayashi, Kenta, Tsuchiya, Takuya},
journal = {Applications of Mathematics},
keywords = {finite element method; triangulation; minimum and maximum angle condition; shape regularity condition; bad triangles},
language = {eng},
number = {5},
pages = {571-588},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Error estimation for finite element solutions on meshes that contain thin elements},
url = {http://eudml.org/doc/299321},
volume = {69},
year = {2024},
}

TY - JOUR
AU - Kobayashi, Kenta
AU - Tsuchiya, Takuya
TI - Error estimation for finite element solutions on meshes that contain thin elements
JO - Applications of Mathematics
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 69
IS - 5
SP - 571
EP - 588
AB - 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 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.
LA - eng
KW - finite element method; triangulation; minimum and maximum angle condition; shape regularity condition; bad triangles
UR - http://eudml.org/doc/299321
ER -

References

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