Two order superconvergence of finite element methods for Sobolev equations

We consider finite element methods applied to a class of Sobolev equations in Rd(d ≥ 1). Global strong superconvergence, which only requires that partitions are quasi-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 in W1, p(Ω) and Lp(Ω) for 2 ≤ p < ∞.