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

Published online by Cambridge University Press:  11 April 2012

Sergey I. Repin ,
Tatiana S. Samrowski  and
Stéfan A. Sauter
Sergey I. Repin
Affiliation:
V.A. Steklov Institute of Mathematics, Russian Academy of Sciences, Fontanka 27, 191023 St. Petersburg, Russia. repin@pdmi.ras.ru
Tatiana S. Samrowski
Affiliation:
Institut für Mathematik, Universität Zürich, 8057 Zürich, Switzerland; tatiana.samrowski@math.uzh.ch; stas@math.uzh.ch
Stéfan A. Sauter
Affiliation:
Institut für Mathematik, Universität Zürich, 8057 Zürich, Switzerland; tatiana.samrowski@math.uzh.ch; stas@math.uzh.ch
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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.

Keywords

A posteriori error estimatecomplicated diffusion coefficientdefeaturing of modelscombined modeling discretization adaptive strategy
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 46 , Issue 6 , November 2012 , pp. 1389 - 1405
Copyright
© EDP Sciences, SMAI, 2012

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