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A Reduced Basis Method for Parametrized Variational Inequalities

dc.contributor.authorHaasdonk, Bernard
dc.contributor.authorSalomon, Julien
HAL ID: 738224
dc.contributor.authorWohlmuth, Barbara
dc.date.accessioned2013-06-24T07:47:25Z
dc.date.available2013-06-24T07:47:25Z
dc.date.issued2012
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/11477
dc.language.isoenen
dc.subjectmodel reductionen
dc.subjectreduced basis methodsen
dc.subjectvariational inequalitiesen
dc.subjecta posteriori error boundsen
dc.subject.ddc515en
dc.titleA Reduced Basis Method for Parametrized Variational Inequalitiesen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenReduced basis methods are an efficient tool for significantly reducing the computational complexity of solving parametrized PDEs. Originally introduced for elliptic equations, they have been generalized during the last decade to various types of elliptic, parabolic, and hyperbolic systems. In this article, we extend the reduction technique to parametrized variational inequalities. First, we propose a reduced basis variational inequality scheme in a saddle point form and prove existence and uniqueness of the solution. We state some elementary analytical properties of the scheme such as reproduction of solutions, a priori stability with respect to the data, and Lipschitz-continuity with respect to the parameters. An offline/online decomposition guarantees an efficient assembling of the reduced scheme, which can be solved by constrained quadratic programming. Second, we provide rigorous a posteriori error bounds with a partial offline/online decomposition. The reduction scheme is applied to one-dimensional obstacle problems. The numerical results confirm the theoretical ones and demonstrate the efficiency of the reduction technique.en
dc.relation.isversionofjnlnameSIAM Journal on Numerical Analysis
dc.relation.isversionofjnlvol50en
dc.relation.isversionofjnlissue5en
dc.relation.isversionofjnldate2012
dc.relation.isversionofjnlpages2656-2676en
dc.relation.isversionofdoihttp://dx.doi.org/10.1137/110835372en
dc.relation.isversionofjnlpublisherSIAMen
dc.subject.ddclabelAnalyseen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen


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