Reduced basis a posteriori error bounds for the stokes equations in parametrized domains: A penalty approach

Anna Lena Gerner, Karen Veroy

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

14 Citaten (Scopus)

Samenvatting

We present reduced basis approximations and associated rigorous a posteriori error bounds for the Stokes equations in parametrized domains. The method, built upon the penalty formulation for saddle point problems, provides error bounds not only for the velocity but also for the pressure approximation, while simultaneously admitting affine geometric variations with relative ease. The essential ingredients are: (i) dimension reduction through Galerkin projection onto a low-dimensional reduced basis space; (ii) stable, good approximation of the pressure through supremizer-enrichment of the velocity reduced basis space; (iii) optimal and numerically stable approximations identified through an efficient greedy sampling method; (iv) certainty, through rigorous a posteriori bounds for the errors in the reduced basis approximation; and (v) efficiency, through an offline-online computational strategy. The method is applied to a flow problem in a two-dimensional channel with a (parametrized) rectangular obstacle. Numerical results show that the reduced basis approximation converges rapidly, the effectivities associated with the (inexpensive) rigorous a posteriori error bounds remain good even for reasonably small values of the penalty parameter, and that the effects of the penalty parameter are relatively benign.

Originele taal-2Engels
Pagina's (van-tot)2103-2134
Aantal pagina's32
TijdschriftMathematical Models and Methods in Applied Sciences
Volume21
Nummer van het tijdschrift10
DOI's
StatusGepubliceerd - okt 2011
Extern gepubliceerdJa

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Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.

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