Incomplete iterations in multistep backward difference methods for parabolic problems with smooth and nonsmooth data
TL;DR: The case when the backward difference equations are only solved 'approximately' by a preconditioned iteration is analyzed, which shows that these methods remain stable and accurate if a suitable number of iterations are used.
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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 nonsmooth initial data cases. Finally, the results of numerical experiments illustrating the algorithms' performance on model problems are given.
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Citations
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C. William Gear
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4.1K
•Book
Galerkin Finite Element Methods for Parabolic Problems
Vidar Thomée
- 01 Jun 1984
TL;DR: The standard Galerkin method is based on more general approximations of the elliptic problem as discussed by the authors, and is used to solve problems in algebraic systems at the time level.
2.2K