Anisotropic finite elements for elliptic problems with singular data

Abstract

We study the problem $-\Delta u=\gamma$, where $\gamma$ is a singular measure, with support on a curve or a point. We prove that optimal rates of convergence for the finite element method can be obtained using properly graded meshes. In particular, we consider isotropic graded meshes when $\gamma$ is a point Dirac delta, and anisotropic graded meshes when $\gamma$ is a measure supported on a segment. Numerical experiments are shown that verify our results, and lead to interesting observations.

26 Pages. 3 Figures, 5 Tables

References in corpus (1)

• The Representation of Line Dirac Delta Function Along a Space Curve