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Mathematics of Computation

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Adaptive multilevel methods in space and time
for parabolic problems-the periodic case

Authors: J. B. Burie and M. Marion
Journal: Math. Comp. 69 (2000), 547-581
MSC (1991): Primary 65M15, 65M70, 65B99
Published electronically: March 3, 1999
MathSciNet review: 1648359
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Abstract: The aim of this paper is to display numerical results that show the interest of some multilevel methods for problems of parabolic type. These schemes are based on multilevel spatial splittings and the use of different time steps for the various spatial components. The spatial discretization we investigate is of spectral Fourier type, so the approximate solution naturally splits into the sum of a low frequency component and a high frequency one. The time discretization is of implicit/explicit Euler type for each spatial component. Based on a posteriori estimates, we introduce adaptive one-level and multilevel algorithms. Two problems are considered: the heat equation and a nonlinear problem. Numerical experiments are conducted for both problems using the one-level and the multilevel algorithms. The multilevel method is up to 70% faster than the one-level method.

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Additional Information

J. B. Burie
Affiliation: UPRESA S466, Mathématiques Appliquées de Bordeaux, Université Victor Segalen Bordeaux 2, BP26, 146 rue Léo-Saignat, 33076 Bordeaux Cedex, France

M. Marion
Affiliation: UMR CNRS 5585 et Département Mathématiques–Informatique, Ecole Centrale de Lyon, BP 163, 69131 ECULLY Cedex, France

Keywords: Multilevel methods, Fourier Galerkin, parabolic equations, a posteriori error estimates, adaptive algorithms
Received by editor(s): October 15, 1997
Received by editor(s) in revised form: April 14, 1998
Published electronically: March 3, 1999
Article copyright: © Copyright 2000 American Mathematical Society

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