Reduced Basis Approximation for Shape Optimization in Thermal Flows with a Parametrized Polynomial Geometric Map

Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 76)

Abstract

Reduced basis approximations for geometrically parametrized advection-diffusion equations are investigated. The parametric domains are assumed to be images of a reference domain through a piecewise polynomial map; this may lead to nonaffinely parametrized diffusion tensors that are treated with an empirical interpolation method. An a posteriori error bound including a correction term due to this approximation is given. Results concerning the applied methodology and the rigor of the corrected error estimator are shown for a shape optimization problem in a thermal flow.

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Copyright information

© Springer Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.MATHICSE-CMCS Modelling and Scientific ComputingÉcole Polytechnique Fédérale de LausanneLausanneSwitzerland
  2. 2.Institute of MathematicsHelsinki University of TechnologyHelsinkiFinland

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