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Finite element approximation of a parabolic integro-differential equation with a weakly singular kernel

Authors: C. Chen, V. Thomée and L. B. Wahlbin
Journal: Math. Comp. 58 (1992), 587-602
MSC: Primary 65M60; Secondary 65R20
MathSciNet review: 1122059
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Abstract: We give error estimates for the numerical solution by means of the Galerkin finite element method of an integro-differential equation of parabolic type with a memory term containing a weakly singular kernel. Optimal-order estimates are shown for spatially semidiscrete and completely discrete methods. Special attention is paid to the regularity of the exact solution.

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Keywords: Parabolic, integro-differential equation, memory, Galerkin, finite element, weakly singular kernel
Article copyright: © Copyright 1992 American Mathematical Society