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

In this note we examine several regularity criteria for families of simplicial finite element partitions in Rd,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.