Incomplete iterations in multistep backward difference methods for parabolic problems with smooth and nonsmooth data

Authors:
James H. Bramble, Joseph E. Pasciak, Peter H. Sammon and Vidar Thomée

Journal:
Math. Comp. **52** (1989), 339-367

MSC:
Primary 65N10; Secondary 65N20

DOI:
https://doi.org/10.1090/S0025-5718-1989-0962207-8

MathSciNet review:
962207

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Abstract: Backward difference methods for the discretization of parabolic boundary value problems are considered in this paper. In particular, we analyze the case when the backward difference equations are only solved 'approximately' by a preconditioned iteration. We provide an analysis which shows that these methods remain stable and accurate if a suitable number of iterations (often independent of the spatial discretization and time step size) are used. Results are provided for the smooth as well as non-smooth initial data cases. Finally, the results of numerical experiments illustrating the algorithms' performance on model problems are given.

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DOI:
https://doi.org/10.1090/S0025-5718-1989-0962207-8

Article copyright:
© Copyright 1989
American Mathematical Society