Combined a posteriori modeling-discretization error estimate for elliptic problems with complicated interfaces

Sergey I. Repin; Tatiana S. Samrowski; Stéfan A. Sauter

ESAIM: Mathematical Modelling and Numerical Analysis (2012)

  • Volume: 46, Issue: 6, page 1389-1405
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Repin, Sergey I., Samrowski, Tatiana S., and Sauter, Stéfan A.. "Combined a posteriori modeling-discretization error estimate for elliptic problems with complicated interfaces." ESAIM: Mathematical Modelling and Numerical Analysis 46.6 (2012): 1389-1405. <http://eudml.org/doc/277846>.

@article{Repin2012,
abstract = {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.},
author = {Repin, Sergey I., Samrowski, Tatiana S., Sauter, Stéfan A.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {A posteriori error estimate; complicated diffusion coefficient; defeaturing of models; combined modeling discretization adaptive strategy; interfaces; modeling error; discretization error; a posteriori estimates; linear diffusion equation; numerical test},
language = {eng},
month = {4},
number = {6},
pages = {1389-1405},
publisher = {EDP Sciences},
title = {Combined a posteriori modeling-discretization error estimate for elliptic problems with complicated interfaces},
url = {http://eudml.org/doc/277846},
volume = {46},
year = {2012},
}

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
DA - 2012/4//
PB - EDP Sciences
VL - 46
IS - 6
SP - 1389
EP - 1405
AB - 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.
LA - eng
KW - A posteriori error estimate; complicated diffusion coefficient; defeaturing of models; combined modeling discretization adaptive strategy; interfaces; modeling error; discretization error; a posteriori estimates; linear diffusion equation; numerical test
UR - http://eudml.org/doc/277846
ER -

References

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