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