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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 spatially discrete approximations of semilinear parabolic equations with nonsmooth initial data
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by Claes Johnson, Stig Larsson, Vidar Thomée and Lars B. Wahlbin PDF
Math. Comp. 49 (1987), 331-357 Request permission

Abstract:

We consider time-continuous spatially discrete approximations by the Galerkin finite element method of initial-boundary value problems for semilinear parabolic equations with nonsmooth or incompatible initial data. We find that the numerical solution enjoys a gain in accuracy at positive time of essentially two orders relative to the initial regularity, as a result of the smoothing property of the parabolic evolution operator. For higher-order elements the restriction to two orders is in contrast to known optimal order results in the linear case.
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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Math. Comp. 49 (1987), 331-357
  • MSC: Primary 65N10; Secondary 65N30
  • DOI: https://doi.org/10.1090/S0025-5718-1987-0906175-1
  • MathSciNet review: 906175