Convergence estimates for product iterative methods with applications to domain decomposition

Authors:
James H. Bramble, Joseph E. Pasciak, Jun Ping Wang and Jinchao Xu

Journal:
Math. Comp. **57** (1991), 1-21

MSC:
Primary 65J10; Secondary 65M55, 65N22, 65N55

MathSciNet review:
1090464

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Abstract: In this paper, we consider iterative methods for the solution of symmetric positive definite problems on a space which are defined in terms of products of operators defined with respect to a number of subspaces. The simplest algorithm of this sort has an error-reducing operator which is the product of orthogonal projections onto the complement of the subspaces. New norm-reduction estimates for these iterative techniques will be presented in an abstract setting. Applications are given for overlapping Schwarz algorithms with many subregions for finite element approximation of second-order elliptic problems.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1991-1090464-8

Keywords:
Second-order elliptic equation,
domain decomposition

Article copyright:
© Copyright 1991
American Mathematical Society