International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 345196, 16 pages
doi:10.1155/2009/345196
Research Article

Strong Superconvergence of Finite Element Methods for Linear Parabolic Problems

Kening Wang1 and Shuang Li2

1Department of Mathematics and Statistics, University of North Florida, Jacksonville, FL 32224, USA
2Derivative Valuation Center, Ernst & Young LLP., New York, NY 10036, USA

Received 30 March 2009; Revised 16 June 2009; Accepted 5 July 2009

Academic Editor: Thomas Witelski

Copyright © 2009 Kening Wang and Shuang Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.