A Posteriori Estimation of Dimension Reduction Errors
نویسندگان
چکیده
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. Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: https://doi.org/10.5167/uzh-21819 Accepted Version Originally published at: Repin, S; Sauter, S; Smolianski, A (2004). A posteriori estimation of dimension reduction errors. In: Feistauer, M. Numerical mathematics and advanced applications. Berlin: Springer, 716-725. A Posteriori Estimation of Dimension Reduction Errors Sergey Repin, Stefan Sauter and Anton Smolianski 1 V.A. Steklov Institute of Mathematics, Fontanka 27, 191 011 St. Petersburg, Russia [email protected] 2 Institute of Mathematics, Zurich University, CH-8057, Zurich, Switzerland stas, [email protected]
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