Über die punktweise Konvergenz Finiter Elemente

Summary

The solution of the Dirichlet problem for Poissons equation −δu=f in a two dimensional convex polyhedral domain Ω is approximated by the simplest finite element method, where the trial functions are linear in triangles of maximal diameterh. The convergence rate in certain weighted Sobolev spaces is established. It follows that for everyx∈Ω, the rate of convergence inx ish ^2−ε with arbitrary small ε>0, iff∈L ₂(Ω) andf bounded in a neighbourhood ofx. This estimate is close to theh ²-accuracy observed in practical calculations.