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A posteriori error estimates for linear exterior problemsvia mixed-FEM and DtN mappings

Published online by Cambridge University Press:  15 May 2002

Mauricio A. Barrientos ,
Gabriel N. Gatica  and
Matthias Maischak
Mauricio A. Barrientos
Affiliation:
GIMA, Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile. mbarrien@ing-mat.udec.cl.
Gabriel N. Gatica
Affiliation:
GIMA, Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile. ggatica@ing-mat.udec.cl.
Matthias Maischak
Affiliation:
Institut für Angewandte Mathematik, Universität Hannover, Welfengarten 1, 30167 Hannover, Germany. maischak@ifam.uni-hannover.de.
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Abstract

In this paper we combine the dual-mixed finite element method with a Dirichlet-to-Neumann mapping (given in terms of a boundary integral operator) to solve linear exterior transmission problems in the plane. As a model we consider a second order elliptic equation in divergence form coupled with the Laplace equation in the exterior unbounded region. We show that the resulting mixed variational formulation and an associated discrete scheme using Raviart-Thomas spaces are well posed, and derive the usual Cea error estimate and the corresponding rate of convergence. In addition, we develop two different a-posteriori error analyses yielding explicit residual and implicit Bank-Weiser type reliable estimates, respectively. Several numerical results illustrate the suitability of these estimators for the adaptive computation of the discrete solutions.

Keywords

Dirichlet-to-Neumann mappingmixed finite elementsRaviart-Tho mas spacesresidual based estimatesBank-Weiser approach.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 36 , Issue 2 , March 2002 , pp. 241 - 272
Copyright
© EDP Sciences, SMAI, 2002

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