Convergence of some adaptive FEM-BEM coupling for elliptic but possibly nonlinear interface problems

Markus Aurada; Michael Feischl; Dirk Praetorius

ESAIM: Mathematical Modelling and Numerical Analysis (2012)

  • Volume: 46, Issue: 5, page 1147-1173
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Aurada, Markus, Feischl, Michael, and Praetorius, Dirk. "Convergence of some adaptive FEM-BEM coupling for elliptic but possibly nonlinear interface problems." ESAIM: Mathematical Modelling and Numerical Analysis 46.5 (2012): 1147-1173. <http://eudml.org/doc/276389>.

@article{Aurada2012,
abstract = {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.},
author = {Aurada, Markus, Feischl, Michael, Praetorius, Dirk},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {FEM-BEM coupling; a posteriori error estimate; adaptive algorithm; convergence; a posteriori error estimate; symmetric coupling; (nonlinear) interface problem; 2D Laplacian; lowest-order Galerkin scheme; finite element method; boundary element method},
language = {eng},
month = {2},
number = {5},
pages = {1147-1173},
publisher = {EDP Sciences},
title = {Convergence of some adaptive FEM-BEM coupling for elliptic but possibly nonlinear interface problems},
url = {http://eudml.org/doc/276389},
volume = {46},
year = {2012},
}

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
DA - 2012/2//
PB - EDP Sciences
VL - 46
IS - 5
SP - 1147
EP - 1173
AB - 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.
LA - eng
KW - FEM-BEM coupling; a posteriori error estimate; adaptive algorithm; convergence; a posteriori error estimate; symmetric coupling; (nonlinear) interface problem; 2D Laplacian; lowest-order Galerkin scheme; finite element method; boundary element method
UR - http://eudml.org/doc/276389
ER -

References

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