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

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 L p ( 2 ≤ p ≤ ∞ ) norm, second order in W 1 , p ( 2 ≤ p ≤ ∞ ) norm and almost second order in W 1 , ∞ norm. For k = 1 , we obtain first order gain in W 1 , 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 L p and W 1 , p ( 2 ≤ p ≤ ∞ ) .