Volume 53, Number 6, November-December 2019
|Page(s)||1871 - 1891|
|Published online||18 October 2019|
Finite element method with local damage of the mesh⋆
Sorbonne Universités, UPMC Univ Paris 06, CNRS UMR 7598, Laboratoire Jacques-Louis Lions, 75005 Paris, France
2 IMAG, Univ Montpellier, CNRS, Montpellier, France
3 Laboratoire de Mathématiques de Besançon, UMR CNRS 6623, Université Bourgogne Franche-Comté, 16, Route de Gray, 25030 Besançon Cedex, France
* Corresponding author: firstname.lastname@example.org
Accepted: 13 March 2019
We consider the finite element method on locally damaged meshes allowing for some distorted cells which are isolated from one another. In the case of the Poisson equation and piecewise linear Lagrange finite elements, we show that the usual a priori error estimates remain valid on such meshes. We also propose an alternative finite element scheme which is optimally convergent and, moreover, well conditioned, i.e. the conditioning number of the associated finite element matrix is of the same order as that of a standard finite element method on a regular mesh of comparable size.
Mathematics Subject Classification: 65N30 / 65N12 / 65N15
Key words: Finite elements / mesh quality / a priori estimates / conditioning
© The authors. Published by EDP Sciences, SMAI 2019
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