Finite element method with local damage on the mesh
Provides theoretical justification and a practical method for using finite elements on meshes with local damage, benefiting computational mechanics practitioners who encounter imperfect meshes.
The authors prove that standard a priori error estimates for the Poisson equation with piecewise linear finite elements remain valid on meshes with isolated distorted cells, and propose an alternative scheme that is optimally convergent and well-conditioned.
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.