Two order superconvergence of finite element methods for Sobolev equations

Abstract

We consider finite element methods applied to a class of Sobolev equations inRd(d ≥ 1). Global strong superconvergence, which only requires that partitions are quais-uniform, is investigated for the error between the approximate solution and the Ritz-Sobolev projection of the exact solution. Two order superconvergence results are demonstrated inW1,p(Ω) andLp(Ω) for 2 ≤p < ∞.