Strong Superconvergence of Finite Element Methods for Linear Parabolic Problems

We study the strong superconvergence of a semidiscrete finite element scheme for linear parabolic problems on Q = Ω × (0, T], where Ω is a bounded domain in ℛd (d ≤ 4) with piecewise smooth boundary. We establish the global two order superconvergence results for the error between the approximate solution and the Ritz projection of the exact solution of our model problem in W1,p(Ω) and Lp(Q) with 2 ≤ p < ∞ and the almost two order superconvergence in W1,∞(Ω) and L∞(Q). Results of the p = ∞ case are also included in two space dimensions (d = 1 or 2). By applying the interpolated postprocessing technique, similar results are also obtained on the error between the interpolation of the approximate solution and the exact solution.