On generalizations of the Synge-Křížek maximum angle condition for $d$-simplices

Abstract

In this note we present a generalization of the maximum angle condition, proposed by J. L. Synge in 1957 and M. Křížek in 1992 for triangular and tetrahedral elements, respectively, for the case of higher-dimensional simplicial finite elements. Its relations to the other angle-type conditions commonly used in finite element methods are analysed.