## When does the finite element method converge?

- ID: 2703, RIV: 10314915
- ISSN: not specified, ISBN: 978-80-86407-55-5
- source: SNA'15 Seminar on Numerical Analysis
- keywords: Finite element method; maximum angle condition
- authors: Václav Kučera
- authors from KNM: Strakoš Zdeněk, Kučera Václav

### Abstract

The well-known maximum angle condition, [3], gives us O(h) convergence of the piecewise linear finite element method. In [2], it is shown by a simple argument, that this condition is not necessary, only sufficient. While the necessary and sufficient condition remains unknown, we generalize the maximum angle condition, so that degenerating elements are allowed, as long as they form clusters of diameter at most O(h) which are at least O(h) apart.