Optimal <i>a priori</i> error estimates in weighted Sobolev spaces for the Poisson problem with singular sources

We study the problem -? u = f , where has a point-singularity. In particular, we are interested in ? x 0 Dirac delta with support but singularities of form ~ | ? ?s also considered. prove stability Galerkin projection on graded meshes weighted spaces, weights given by powers distance to . recover optimal rates convergence for finite element method these meshes. Our approach is general and holds both two three dimensions. Numerical experiments shown that verify our results, lead interesting observations.