Variational multiscale proper orthogonal decomposition: Convection-dominated convection-diffusion-reaction equations

Iliescu, Traian; Wang, Zhu

doi:10.1090/S0025-5718-2013-02683-X

Variational multiscale proper orthogonal decomposition: Convection-dominated convection-diffusion-reaction equations
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by Traian Iliescu and Zhu Wang

Math. Comp. 82 (2013), 1357-1378

DOI: https://doi.org/10.1090/S0025-5718-2013-02683-X

Published electronically: March 18, 2013

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Abstract:

We introduce a variational multiscale closure modeling strategy for the numerical stabilization of proper orthogonal decomposition reduced-order models of convection-dominated equations. As a first step, the new model is analyzed and tested for convection-dominated convection-diffusion-reaction equations. The numerical analysis of the finite element discretization of the model is presented. Numerical tests show the increased numerical accuracy over the standard reduced-order model and illustrate the theoretical convergence rates.

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