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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

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Nonsmooth data error estimates for approximations of an evolution equation with a positive-type memory term
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by Ch. Lubich, I. H. Sloan and V. Thomée PDF
Math. Comp. 65 (1996), 1-17 Request permission

Abstract:

We study the numerical approximation of an integro-differential equation which is intermediate between the heat and wave equations. The proposed discretization uses convolution quadrature based on the first- and second-order backward difference methods in time, and piecewise linear finite elements in space. Optimal-order error bounds in terms of the initial data and the inhomogeneity are shown for positive times, without assumptions of spatial regularity of the data.
References
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Additional Information
  • Ch. Lubich
  • Affiliation: Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, Germany
  • MR Author ID: 116445
  • Email: lubich@na.mathematik.uni-tuebingen.de
  • I. H. Sloan
  • Affiliation: School of Mathematics, University of New South Wales, Sydney 2052, Australia
  • MR Author ID: 163675
  • ORCID: 0000-0003-3769-0538
  • Email: I.Sloan@unsw.edu.au
  • V. Thomée
  • Affiliation: Department of Mathematics, Chalmers University of Technology, S-412 96 Göteborg, Sweden
  • MR Author ID: 172250
  • Email: thomee@math.chalmers.se
  • Received by editor(s): August 30, 1994
  • © Copyright 1996 American Mathematical Society
  • Journal: Math. Comp. 65 (1996), 1-17
  • MSC (1991): Primary 45K05, 65M60, 65D32
  • DOI: https://doi.org/10.1090/S0025-5718-96-00677-1
  • MathSciNet review: 1322891