International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 5, Pages 343-359

Superconvergence of a finite element method for linear integro-differential problems

Do Y. Kwak,1 Sungyun Lee,1 and Qian Li2

1Department of Mathematics, Kaist, Taejon 305-701, Korea
2Department of Mathematics, Shandong Normal University, Shandong, Jinan 250014, China

Received 10 September 1998

Copyright © 2000 Do Y. Kwak et al. 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.


We introduce a new way of approximating initial condition to the semidiscrete finite element method for integro-differential equations using any degree of elements. We obtain several superconvergence results for the error between the approximate solution and the Ritz-Volterra projection of the exact solution. For k>1, we obtain first order gain in Lp(2p) norm, second order in W1,p(2p) norm and almost second order in W1, norm. For k=1, we obtain first order gain in W1,p(2p) norms. Further, applying interpolated postprocessing technique to the approximate solution, we get one order global superconvergence between the exact solution and the interpolation of the approximate solution in the Lp and W1,p(2p).