We consider linear elliptic problems with variable coefficients, which may sharply change values and have a complex behavior in the domain. For these problems, a new combined discretization-modeling strategy is suggested and studied. It uses a sequence of simplified models, approximating the original one with increasing accuracy. Boundary value problems generated by these simplified models are solved numerically, and the approximation and modeling errors are estimated by a posteriori estimates of functional type. An efficient numerical strategy is based upon balancing the modeling and discretization errors, which provides an economical way of finding an approximate solution with an a priori given accuracy. Numerical tests demonstrate the reliability and efficiency of this combined modeling-discretization method.
Mots-clés : a posteriori error estimate, complicated diffusion coefficient, defeaturing of models, combined modeling discretization adaptive strategy
@article{M2AN_2012__46_6_1389_0,
author = {Repin, Sergey I. and Samrowski, Tatiana S. and Sauter, St\'efan A.},
title = {Combined \protect\emph{a posteriori }modeling-discretization error estimate for elliptic problems with complicated interfaces},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1389--1405},
publisher = {EDP-Sciences},
volume = {46},
number = {6},
year = {2012},
doi = {10.1051/m2an/2012007},
zbl = {1281.65144},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an/2012007/}
}
TY - JOUR AU - Repin, Sergey I. AU - Samrowski, Tatiana S. AU - Sauter, Stéfan A. TI - Combined a posteriori modeling-discretization error estimate for elliptic problems with complicated interfaces JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2012 SP - 1389 EP - 1405 VL - 46 IS - 6 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an/2012007/ DO - 10.1051/m2an/2012007 LA - en ID - M2AN_2012__46_6_1389_0 ER -
%0 Journal Article %A Repin, Sergey I. %A Samrowski, Tatiana S. %A Sauter, Stéfan A. %T Combined a posteriori modeling-discretization error estimate for elliptic problems with complicated interfaces %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2012 %P 1389-1405 %V 46 %N 6 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an/2012007/ %R 10.1051/m2an/2012007 %G en %F M2AN_2012__46_6_1389_0
Repin, Sergey I.; Samrowski, Tatiana S.; Sauter, Stéfan A. Combined a posteriori modeling-discretization error estimate for elliptic problems with complicated interfaces. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 46 (2012) no. 6, pp. 1389-1405. doi : 10.1051/m2an/2012007. http://archive.numdam.org/articles/10.1051/m2an/2012007/
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