International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 5, Pages 343-359
doi:10.1155/S0161171200001940
Abstract
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(2≤p≤∞) norm, second order in W1,p(2≤p≤∞) norm and almost second order in W1,∞ norm. For k=1, we obtain first order gain in W1,p(2≤p≤∞) 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(2≤p≤∞).