# $\mathit{A}$-$\mathrm{\mathit{P}\mathit{O}\mathit{S}\mathit{T}\mathit{E}\mathit{R}\mathit{I}\mathit{O}\mathit{R}\mathit{I}}$ error estimates for linear exterior problems $\mathrm{\mathit{V}\mathit{I}\mathit{A}}$ mixed-FEM and DtN mappings

Mauricio A. Barrientos; Gabriel N. Gatica; Matthias Maischak

- Volume: 36, Issue: 2, page 241-272
- ISSN: 0764-583X

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topBarrientos, Mauricio A., Gatica, Gabriel N., and Maischak, Matthias. "${\it A}$-${\it POSTERIORI}$ error estimates for linear exterior problems ${\it VIA}$ mixed-FEM and DtN mappings." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 36.2 (2002): 241-272. <http://eudml.org/doc/245337>.

@article{Barrientos2002,

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.},

author = {Barrientos, Mauricio A., Gatica, Gabriel N., Maischak, Matthias},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {Dirichlet-to-Neumann mapping; mixed finite elements; Raviart-Thomas spaces; residual based estimates; Bank-Weiser approach; linear exterior transmission problems; second order elliptic equations; Laplace equation; unbounded region; error estimate; convergence; numerical estimate; performance},

language = {eng},

number = {2},

pages = {241-272},

publisher = {EDP-Sciences},

title = {$\{\it A\}$-$\{\it POSTERIORI\}$ error estimates for linear exterior problems $\{\it VIA\}$ mixed-FEM and DtN mappings},

url = {http://eudml.org/doc/245337},

volume = {36},

year = {2002},

}

TY - JOUR

AU - Barrientos, Mauricio A.

AU - Gatica, Gabriel N.

AU - Maischak, Matthias

TI - ${\it A}$-${\it POSTERIORI}$ error estimates for linear exterior problems ${\it VIA}$ mixed-FEM and DtN mappings

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2002

PB - EDP-Sciences

VL - 36

IS - 2

SP - 241

EP - 272

AB - 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.

LA - eng

KW - Dirichlet-to-Neumann mapping; mixed finite elements; Raviart-Thomas spaces; residual based estimates; Bank-Weiser approach; linear exterior transmission problems; second order elliptic equations; Laplace equation; unbounded region; error estimate; convergence; numerical estimate; performance

UR - http://eudml.org/doc/245337

ER -

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