On the equivalence of regularity criteria for triangular and tetrahedral finite element partitions

Authors:
Jan Brandts;Sergey Korotov;Michal Kříek
Affiliations:
Korteweg-de Vries Institute, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, Netherlands;Institute of Mathematics, Helsinki University of Technology, P.O.Box 1100, FI-02015 TKK, Finland;Institute of Mathematics, Academy of Sciences, itná 25, CZ-115 67 Prague 1, Czech Republic
Venue:
Computers & Mathematics with Applications
Year:
2008

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Abstract

In this note we examine several regularity criteria for families of simplicial finite element partitions in R^d,d@?{2,3}. These are usually required in numerical analysis and computer implementations. We prove the equivalence of four different definitions of regularity often proposed in the literature. The first one uses the volume of simplices. The others involve the inscribed and circumscribed ball conditions, and the minimal angle condition.