2018/08/20 by Michel Duprez, Duprez, Michel, Vanessa Lleras +3
Engineering · #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · doi:10.48550/arxiv.1808.06350
openalex publication_date 2018/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.