Volume 36, Number 2, March/April 2002
|Page(s)||241 - 272|
|Published online||15 May 2002|
A posteriori error estimates for linear exterior problems via mixed-FEM and DtN mappings
GIMA, Departamento de Ingeniería Matemática,
Universidad de Concepción, Casilla 160-C, Concepción, Chile. email@example.com.
2 GIMA, Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile. firstname.lastname@example.org.
3 Institut für Angewandte Mathematik, Universität Hannover, Welfengarten 1, 30167 Hannover, Germany. email@example.com.
Revised: 8 January 2002
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.
Mathematics Subject Classification: 65N15 / 65N30 / 65N38 / 65N50
Key words: Dirichlet-to-Neumann mapping / mixed finite elements / Raviart-Tho mas spaces / residual based estimates / Bank-Weiser approach.
© EDP Sciences, SMAI, 2002
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