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 L 2-error estimate of order for the semidiscrete solution when the given initial function is only in L 2. 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 ∞(L 2). 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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Received: December 1998 / Revised version: January 2000
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Pani, A., Sinha, R. Error estimates for semidiscrete Galerkin approximation to a time dependent parabolic integro-differential equation with nonsmooth data. CALCOLO 37, 181–205 (2000). https://doi.org/10.1007/s100920070001
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DOI: https://doi.org/10.1007/s100920070001