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≤∞).
