Finite element method with local damage of the mesh
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 53 (2019) no. 6, pp. 1871-1891.

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.

DOI : 10.1051/m2an/2019023
Classification : 65N30, 65N12, 65N15
Mots-clés : Finite elements, mesh quality, a priori estimates, conditioning
Duprez, Michel 1 ; Lleras, Vanessa 1 ; Lozinski, Alexei 1

1 
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     title = {Finite element method with local damage of the mesh},
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Duprez, Michel; Lleras, Vanessa; Lozinski, Alexei. Finite element method with local damage of the mesh. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 53 (2019) no. 6, pp. 1871-1891. doi : 10.1051/m2an/2019023. http://www.numdam.org/articles/10.1051/m2an/2019023/

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