Year: 2010
Journal of Computational Mathematics, Vol. 28 (2010), Iss. 1 : pp. 122–148
Abstract
In this work we consider the Reduced Basis method for the solution of parametrized advection-reaction partial differential equations. For the generation of the basis we adopt a stabilized finite element method and we define the Reduced Basis method in the "primal-dual" formulation for this stabilized problem. We provide a priori Reduced Basis error estimates and we discuss the effects of the finite element approximation on the Reduced Basis error. We propose an adaptive algorithm, based on the a posteriori Reduced Basis error estimate, for the selection of the sample sets upon which the basis are built; the idea leading this algorithm is the minimization of the computational costs associated with the solution of the Reduced Basis problem. Numerical tests demonstrate the efficiency, in terms of computational costs, of the "primal-dual" Reduced Basis approach with respect to an "only primal" one.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2009.09-m3015
Journal of Computational Mathematics, Vol. 28 (2010), Iss. 1 : pp. 122–148
Published online: 2010-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 27
Keywords: Parametrized advection–reaction partial differential equations Reduced Basis method “primal–dual” reduced basis approach Stabilized finite element method a posteriori error estimation.
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