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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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


Authors: Traian Iliescu and Zhu Wang
Journal: Math. Comp. 82 (2013), 1357-1378
MSC (2010): Primary 76F65, 65M60; Secondary 76F20, 65M15
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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Additional Information

Traian Iliescu
Affiliation: Department of Mathematics, Virginia Polytechnic Institute and State University, 456 McBryde Hall, Blacksburg, Virginia 24061
Email: iliescu@vt.edu

Zhu Wang
Affiliation: Department of Mathematics, Virginia Polytechnic Institute and State University, 407E McBryde Hall, Blacksburg, Virginia 24061
Email: wangzhu@vt.edu

DOI: http://dx.doi.org/10.1090/S0025-5718-2013-02683-X
PII: S 0025-5718(2013)02683-X
Keywords: Proper orthogonal decomposition, variational multiscale
Received by editor(s): November 23, 2010
Received by editor(s) in revised form: December 2, 2011
Published electronically: March 18, 2013
Additional Notes: The first author was supported in part by NSF Grants #DMS-0513542 and #OCE-0620464 and AFOSR grant #FA9550-08-1-0136
The second author was supported in part by NSF Grants #DMS-0513542 and #OCE-0620464 and AFOSR grant #FA9550-08-1-0136.
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.