A note on necessary and sufficient conditions for convergence of the finite element method

Abstract

In this short note, we present several ideas and observations concerning finite element convergence and the role of the maximum angle condition. Based on previous work, we formulate a hypothesis concerning a necessary condition for O(h) convergence and show a simple relation to classical problems in measure theory and differential geometry which could lead to new insights in the area.

Keywords

• finite element method
• convergence
• maximum angle condition