  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.
