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A posteriori analysis and adaptive error control for operator decomposition solution of coupled semilinear elliptic systems
Author(s) -
Carey V.,
Estep D.,
Tavener S.
Publication year - 2013
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4482
Subject(s) - discretization , iterated function , operator (biology) , discretization error , a priori and a posteriori , mathematics , elliptic operator , decomposition method (queueing theory) , domain decomposition methods , iterative method , decomposition , approximation error , mathematical optimization , computer science , finite element method , mathematical analysis , discrete mathematics , biochemistry , chemistry , philosophy , physics , ecology , epistemology , repressor , biology , transcription factor , gene , thermodynamics
SUMMARY 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 & Sons, Ltd.