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Research Article Open access CC BY 3.0

Asymptotic Domain Decomposition and a Posteriori Estimates for a Semi Linear Problem

Jérôme Pousin, Kamel Slimani

Journal of Advances in Mathematics and Computer Science · pp. 226–241 · Published 8 Dec 2012

10.9734/BJMCS/2012/1632

Abstract

Coupling heterogeneous mathematical models is today commonly used, and effective solution methods for the resulting hybrid problem have recently become available for several systems. Even if in certain circumstances, asymptotic evaluations of the location of the interfaces are available, no strategy are proposed for locating the interfaces in numerical simulations. In this article, a semilinear elliptic problem is considered. By reformulating the problem in a mixed formulation context and by using an a posteriori error estimate, we propose an indicator of the error due to a wrong position of the junction. Minimizing this indicator allows us to determine accurately the location of the junction. By comparing this indicator with a mesh error indicator, this allows to decide if it is better to refine the mesh or to move the interface. Some numerical results are presented showing the efficiency of the proposed indicator.

Method of asymptotic partial domain decomposition a posteriori error estimates Indicator of the error semi linear elliptic equations

References (13)

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Cited by 2

Estimation a posteriori et méthode de décomposition de domaine

Kamel Slimani · 2014

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