The object of this paper is to investigate the convergence of semidiscrete finite element approximations to the parabolic and hyperbolic integral-differential equations ,Sobolev equations and visco-elasticy equations. The Ritz-Volterra projection will be used to unity much of the anal- ysis for the different types of problems.Optimal order error estimates are obtained in Lp and W1p spaces for 2≤p≤∞ .
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