(untitled) (Journal of Computational Mathematics, 2002)
In this paper, we present a general error analysis framework for the finite volume element (FVE) approximation to the Ritz-Volterra projection, the Sobolev equations and parabolic integro-differential equations. The main idea in our paper is to consider the FVE methods as perturbations of standard finite element methods which enables us to derive the optimal L_2 and H^1 norm error estimates, and the L_∞ and W^1_∞ norm error estimates by means of the time dependent Green functions. Our discussions also include elliptic and parabolic problems as the special cases.