Generalization of the Zlámal condition for simplicial finite elements in ℝ d

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

“…In Fig. 4 we observe the practical rates of convergence on F 1 and F 2 for problem (5) with the following right-hand side…”

“…For a generalization of the minimum angle condition into three-dimensional case see [4], and for higher dimensions see e.g. [5,6,8].…”

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

“…One of the most famous uses of the mesh regularity concept is the so-called Zlámal minimum angle condition (see Remark 4 and also [29], [8], [10], [28]), which can be roughly described as a general requirement on triangular elements to guarantee that their shape does not degenerate in the course of refinement.…”

“…The above definition is a natural d-dimensional generalization (see [8]) of the Zlámal minimum angle condition, which is formulated as follows: There exists a constant α 0 such that for any triangulation T h ∈ F and any triangle T ∈ T h we have…”

“…Further (equivalent) definitions of the regularity of a family of partitions of a polytope into simplices are presented in [6], [7].…”