Abstract
In this paper, an attempt has been made to carry over known results for the finite element Galerkin method for a time dependent parabolic equation with nonsmooth initial data to an integro-differential equation of parabolic type. More precisely, for the homogeneous problem a standard energy technique in conjunction with a duality argument is used to obtain an L2-error estimate of order \(\) for the semidiscrete solution when the given initial function is only in L2. Further, for the nonhomogeneous case with zero initial condition, an error estimate of order \(\) uniformly in time is proved, provided that the nonhomogeneous term is in L∞(L2). The present paper provides a complete answer to an open problem posed on p. 106 of the book Finite Element Methods for Integro-differential Equations by Chen and Shih.
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