Graded mesh approximation in weighted Sobolev spaces and elliptic equations in 2D

conformally invariant families of finite elements (no affine invariance is used), stressing the use of elements that lead to higher regularity finite-element spaces. We prove that for a suitable grading of the meshes, one obtains the usual optimal approximation results. We provide a construction of these spaces that does not lead to long, ``skinny'' triangles. Our results are then used to obtain L^2-error estimates and h^m-quasi-optimal rates of convergence for the FEM approximation of solutions of strongly elliptic interface/boundary value problems.]]>