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Combined a posteriori modelling-discretization error estimate for elliptic problems with variable coefficients


Repin, S I; Samrowski, T; Sauter, S (2012). Combined a posteriori modelling-discretization error estimate for elliptic problems with variable coefficients. Mathematical Modelling and Numerical Analysis, 46(6):1389-1405.

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.

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:December 2012
Deposited On:25 Jan 2013 15:33
Last Modified:05 Apr 2016 16:20
Publisher:Cambridge University Press
ISSN:0764-583X
Additional Information:Copyright: Cambridge University Press.
Publisher DOI:https://doi.org/10.1051/m2an/2012007

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