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Pré-Publication, Document De Travail Année : 2018

Finite element method with local damage on the mesh

Michel Duprez
Vanessa Lleras

Résumé

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. its conditioning is of the same order as that of a standard finite element method on a regular mesh of comparable size.
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Dates et versions

hal-01858033 , version 1 (18-08-2018)
hal-01858033 , version 2 (14-03-2019)

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Michel Duprez, Vanessa Lleras, Alexei Lozinski. Finite element method with local damage on the mesh. 2018. ⟨hal-01858033v1⟩
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