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Mathematics of Computation

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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 $\mathcal {V}$ 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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Keywords: Second-order elliptic equation, domain decomposition
Article copyright: © Copyright 1991 American Mathematical Society