Document Type

Article

Publication Date

3-1-1999

Publication Title

SIAM Journal on Numerical Analysis

Abstract

In the first part of the paper, we introduce an overlapping mortar finite element method for solving two-dimensional elliptic problems discretized on overlapping nonmatching grids. We prove an optimal error bound and estimate the condition numbers of certain overlapping Schwarz preconditioned systems for the two-subdomain case. We show that the error bound is independent of the size of the overlap and the ratio of the mesh parameters. In the second part, we introduce three additive Schwarz preconditioned conjugate gradient algorithms based on the trivial and harmonic extensions. We provide estimates for the spectral bounds on the condition numbers of the preconditioned operators. We show that although the error bound is independent of the size of the overlap, the condition number does depend on it. Numerical examples are presented to support our theory.

Volume

36

Issue

2

First Page Number

581

Last Page Number

606

DOI

10.1137/S0036142997323582

Publisher Statement

© 1999, SIAM Publications.

Included in

Mathematics Commons

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