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Article

Kučera, Václav
A note on necessary and sufficient conditions for convergence of the finite element method. (English). In: Brandts, J., Korotov, S., Křížek, M., Segeth, K., Šístek, J. and Vejchodský, T. (eds.): Application of Mathematics 2015, In honor of the birthday anniversaries of Ivo Babuška (90), Milan Práger (85), and Emil Vitásek (85). Proceedings. Prague, November 18-21, 2015. Institute of Mathematics CAS, Prague, 2015. pp. 132-139
MSC: 53A05, 65N15, 65N30 | Zbl 06669925
Keywords:
finite element method; a priori error estimates; maximum angle condition
Summary:
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.
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