On Synge-type angle condition for $d$-simplices

Abstract

Abstract. The maximum angle condition of J. L. Synge was originally introduced in interpolation theory and further used in finite element analysis and applications for triangular and later also for tetrahedral finite element meshes. In this paper we present some of its generalizations to higher-dimensional simplicial elements. In particular, we prove optimal interpolation properties of linear simplicial elements in R d that degenerate in some way.

Preserved Structure Constants for Red Refinements of Product Elements

“…Simplicial partitions satisfying the maximum angle condition are highly desired in numerical analysis for various interpolation and nite element convergence proofs, see e.g. [17,10]. There is another (equivalent) denition of the maximum angle condition in [12].…”

On interpolation error on degenerating prismatic elements

“…According to [21], the associated finite element approximations preserve the optimal interpolation order in the H 1norm under condition (3), which allows to use meshes with tetrahedra having some types of degeneracy [10]. A new generalization of (2) and (3) in the case of simplices of any dimension has been recently proposed in [12].…”