The maximum angle condition is not necessary for convergence of the finite element method

Antti Hannukainen; Sergey Korotov; Michal Křížek

doi:10.1007/s00211-011-0403-2

The maximum angle condition is not necessary for convergence of the finite element method

Antti Hannukainen, Sergey Korotov^*, Michal Křížek

^*Corresponding author for this work

Department of Mathematics and Systems Analysis

Research output: Contribution to journal › Article › Scientific › peer-review

29 Citations (Scopus)

Abstract

We show that the famous maximum angle condition in the finite element analysis is not necessary to achieve the optimal convergence rate when simplicial finite elements are used to solve elliptic problems. This condition is only sufficient. In fact, finite element approximations may converge even though some dihedral angles of simplicial elements tend to π.

Original language	English
Pages (from-to)	79-88
Number of pages	10
Journal	Numerische Mathematik
Volume	120
Issue number	1-6
DOIs	https://doi.org/10.1007/s00211-011-0403-2
Publication status	Published - Jan 2012
MoE publication type	A1 Journal article-refereed

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10.1007/s00211-011-0403-2

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title = "The maximum angle condition is not necessary for convergence of the finite element method",

abstract = "We show that the famous maximum angle condition in the finite element analysis is not necessary to achieve the optimal convergence rate when simplicial finite elements are used to solve elliptic problems. This condition is only sufficient. In fact, finite element approximations may converge even though some dihedral angles of simplicial elements tend to π.",

author = "Antti Hannukainen and Sergey Korotov and Michal K{\v r}{\'i}{\v z}ek",

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