Combined a posteriori modeling-discretization error estimate for elliptic problems with complicated interfaces
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 46 (2012) no. 6, p. 1389-1405

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.

DOI : https://doi.org/10.1051/m2an/2012007
Classification:  35J15,  65N15,  65N30
Keywords: 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 a posteriori modeling-discretization error estimate for elliptic problems with complicated interfaces},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {46},
     number = {6},
     year = {2012},
     pages = {1389-1405},
     doi = {10.1051/m2an/2012007},
     zbl = {1281.65144},
     language = {en},
     url = {http://www.numdam.org/item/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 - Modélisation Mathématique et Analyse Numérique, Volume 46 (2012) no. 6, pp. 1389-1405. doi : 10.1051/m2an/2012007. http://www.numdam.org/item/M2AN_2012__46_6_1389_0/

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