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Mathematics of Computation

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Nonsmooth Data Error Estimates
for Approximations of an Evolution Equation
with a Positive-Type Memory Term

Authors: Ch. Lubich, I. H. Sloan and V. Thomée
Journal: Math. Comp. 65 (1996), 1-17
MSC (1991): Primary 45K05, 65M60, 65D32
MathSciNet review: 1322891
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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.

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Additional Information

Ch. Lubich
Affiliation: Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, Germany

I. H. Sloan
Affiliation: School of Mathematics, University of New South Wales, Sydney 2052, Australia

V. Thomée
Affiliation: Department of Mathematics, Chalmers University of Technology, S-412 96 Göteborg, Sweden

Keywords: Evolution equation, memory term, nonsmooth data, convolution quad\-ra\-ture
Received by editor(s): August 30, 1994
Article copyright: © Copyright 1996 American Mathematical Society