We consider the symmetric FEM-BEM coupling for the numerical solution of a (nonlinear) interface problem for the 2D Laplacian. We introduce some new a posteriori error estimators based on the (h - h/2)-error estimation strategy. In particular, these include the approximation error for the boundary data, which allows to work with discrete boundary integral operators only. Using the concept of estimator reduction, we prove that the proposed adaptive algorithm is convergent in the sense that it drives the underlying error estimator to zero. Numerical experiments underline the reliability and efficiency of the considered adaptive mesh-refinement.
Mots clés : FEM-BEM coupling, a posteriori error estimate, adaptive algorithm, convergence
@article{M2AN_2012__46_5_1147_0,
author = {Aurada, Markus and Feischl, Michael and Praetorius, Dirk},
title = {Convergence of some adaptive {FEM-BEM} coupling for elliptic but possibly nonlinear interface problems},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1147--1173},
publisher = {EDP-Sciences},
volume = {46},
number = {5},
year = {2012},
doi = {10.1051/m2an/2011075},
mrnumber = {2916376},
zbl = {1276.65066},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an/2011075/}
}
TY - JOUR AU - Aurada, Markus AU - Feischl, Michael AU - Praetorius, Dirk TI - Convergence of some adaptive FEM-BEM coupling for elliptic but possibly nonlinear interface problems JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2012 SP - 1147 EP - 1173 VL - 46 IS - 5 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an/2011075/ DO - 10.1051/m2an/2011075 LA - en ID - M2AN_2012__46_5_1147_0 ER -
%0 Journal Article %A Aurada, Markus %A Feischl, Michael %A Praetorius, Dirk %T Convergence of some adaptive FEM-BEM coupling for elliptic but possibly nonlinear interface problems %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2012 %P 1147-1173 %V 46 %N 5 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an/2011075/ %R 10.1051/m2an/2011075 %G en %F M2AN_2012__46_5_1147_0
Aurada, Markus; Feischl, Michael; Praetorius, Dirk. Convergence of some adaptive FEM-BEM coupling for elliptic but possibly nonlinear interface problems. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 46 (2012) no. 5, pp. 1147-1173. doi : 10.1051/m2an/2011075. http://archive.numdam.org/articles/10.1051/m2an/2011075/
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