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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Error estimates for semidiscrete finite element methods for parabolic integro-differential equations
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by Vidar Thomée and Nai Ying Zhang PDF
Math. Comp. 53 (1989), 121-139 Request permission

Abstract:

The purpose of this paper is to attempt to carry over known results for spatially discrete finite element methods for linear parabolic equations to integro-differential equations of parabolic type with an integral kernel consisting of a partial differential operator of order $\beta \leq 2$. It is shown first that this is possible without restrictions when the exact solution is smooth. In the case of a homogeneous equation with nonsmooth initial data $v,v \in {L_2}$, optimal $O({h^r})$ convergence for positive time is possible in general only if $r \leq 4 - \beta$. This depends on the fact that the exact solution is then only in ${H^{4 - \beta }}$.
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Additional Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Math. Comp. 53 (1989), 121-139
  • MSC: Primary 65R20; Secondary 65M60
  • DOI: https://doi.org/10.1090/S0025-5718-1989-0969493-9
  • MathSciNet review: 969493