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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 inthe plane. As a model we consider a second order elliptic equation in divergence form coupled withthe Laplace equation in the exterior unbounded region. We show that the resulting mixed variationalformulation and an associated discrete scheme using Raviart-Thomas spaces are well posed, and derivethe usual Cea error estimate and the corresponding rate of convergence. In addition, we develop twodifferent a-posteriori error analyses yielding explicit residual and implicit Bank-Weiser typereliable estimates, respectively. Several numerical results illustrate the suitability of theseestimators 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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