# A posteriori error estimates for linear exterior problems via mixed-FEM and DtN mappings

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

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

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

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topBarrientos, Mauricio A., Gatica, Gabriel N., and Maischak, Matthias. "A posteriori error estimates for linear exterior problems via mixed-FEM and DtN mappings." ESAIM: Mathematical Modelling and Numerical Analysis 36.2 (2010): 241-272. <http://eudml.org/doc/194103>.

@article{Barrientos2010,

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},

keywords = {Dirichlet-to-Neumann mapping; mixed finite elements; Raviart-Tho mas spaces;
residual based estimates; Bank-Weiser approach.; 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},

month = {3},

number = {2},

pages = {241-272},

publisher = {EDP Sciences},

title = {A posteriori error estimates for linear exterior problems via mixed-FEM and DtN mappings},

url = {http://eudml.org/doc/194103},

volume = {36},

year = {2010},

}

TY - JOUR

AU - Barrientos, Mauricio A.

AU - Gatica, Gabriel N.

AU - Maischak, Matthias

TI - A posteriori error estimates for linear exterior problems via mixed-FEM and DtN mappings

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

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-Tho mas spaces;
residual based estimates; Bank-Weiser approach.; 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/194103

ER -

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