Geometrical conditions in the finite element method

Abstract

We give a brief overview of some key moments in the history of geometrical conditions ensuring finite element convergence. Starting from the pioneering work of Zlámal and Ženíšek and their minimal angle condition, continuing with the maximal angle condition and the realization of its non-necessity for finite element convergence, we present the newest development in this area, when these geometric conditions can be circumvented in certain situations.