Volume 46, Number 6, November-December 2012
|Page(s)||1389 - 1405|
|Published online||11 April 2012|
Combined a posteriori modeling-discretization error estimate for elliptic problems with complicated interfaces
1 V.A. Steklov Institute of Mathematics, Russian Academy of Sciences, Fontanka 27, 191023 St. Petersburg, Russia
2 Institut für Mathematik, Universität Zürich, 8057 Zürich, Switzerland
Received: 27 October 2010
Revised: 7 April 2011
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.
Mathematics Subject Classification: 35J15 / 65N15 / 65N30
Key words: A posteriori error estimate / complicated diffusion coefficient / defeaturing of models / combined modeling discretization adaptive strategy
© EDP Sciences, SMAI, 2012
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