A Posteriori Estimation of Dimension Reduction Errors

Sergey Repin (), Stefan Sauter () and Anton Smolianski ()
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Sergey Repin: V.A. Steklov Institute of Mathematics
Stefan Sauter: Zurich University, Institute of Mathematics
Anton Smolianski: Zurich University, Institute of Mathematics

A chapter in Numerical Mathematics and Advanced Applications, 2004, pp 716-725 from Springer

Abstract: Summary A new a-posteriori error estimator is presented for the verification of the dimensionally reduced models stemming from the elliptic problems on thin domains. The original problem is considered in a general setting, without any specific assumptions on the domain geometry, coefficients and the right-hand sides. The estimator provides a guaranteed upper bound for the modelling error in the energy norm, exhibits the optimal convergence rate as the domain thickness tends to zero and accurately indicates the local error distribution.

Keywords: Elliptic Problem; Posteriori Error; Energy Norm; Posteriori Error Estimation; Dimensional Reduction Method (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-18775-9_70

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DOI: 10.1007/978-3-642-18775-9_70

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