A Posteriori Estimation of Dimension Reduction Errors
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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.
KeywordsElliptic Problem Posteriori Error Energy Norm Posteriori Error Estimation Dimensional Reduction Method
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- 6.Repin, S.I., Sauter, S.A., Smolianski, A.A. (2003): A posteriori error estimation for the Poisson equation with mixed Dirichlet/Neumann boundary conditions. Preprint 02-2003, Institut of Mathematics, Zurich University, http://www.math.unizh.ch/index.php?preprint
- 7.Repin, S.I., Sauter, S.A., Smolianski, A.A. (2003): A posteriori estimation of dimension reduction errors for elliptic problems on thin domains. Preprint 18-2003, Institut of Mathematics, Zurich University, http://www.math.unizh.ch/index.php?preprint