A posteriori analysis and adaptive error control for operator decomposition solution of coupled semilinear elliptic systems. (4th April 2013)

• Record Type: Journal Article
• Authors: Carey, V.; Estep, D.; Tavener, S.
• Is Part Of: International journal for numerical methods in engineering. Volume 94:Number 9(2013)
• Page Start: 826
• Page End: 849
• Publication Date: 2013-04-04
• Subjects: Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.4482
• Languages: English
• ISSNs: 0029-5981

Abstract

<abstract abstract-type="main" id="nme4482-abs-0001"> <title>SUMMARY</title> <p id="nme4482-para-0001">In this paper, we develop an a posteriori error analysis for operator decomposition iteration methods applied to systems of coupled semilinear elliptic problems. The goal is to compute accurate error estimates that account for the combined effects arising from numerical approximation (discretization) and operator decomposition iteration. In an earlier paper, we considered 'triangular' systems that can be solved without iteration. In contrast, operator decomposition iterative methods for fully coupled systems involve an iterative solution technique. We construct an error estimate for the numerical approximation error that specifically addresses the propagation of error between iterates and provide a computable estimate for the iteration error arising because of the decomposition of the operator. Finally, we develop an adaptive discretization strategy to systematically reduce the discretization error.Copyright © 2013 John Wiley &amp; Sons, Ltd.</p> </abstract>