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A posteriori error bounds for reduced-basis approximation of parametrized noncoercive and nonlinear elliptic partial differential equations

Patera, Adolf, 1836-1912, Rovas Dimitrios, C. Prud’homme, Veroy, Karen

Απλή Εγγραφή


URIhttp://purl.tuc.gr/dl/dias/E7230C93-2C9B-4B6F-B93D-5C660B6DA4D8-
Αναγνωριστικόhttp://augustine.mit.edu/methodology/papers/atpAIAA2003.pdf-
Γλώσσαen-
Μέγεθος18 pagesen
ΤίτλοςA posteriori error bounds for reduced-basis approximation of parametrized noncoercive and nonlinear elliptic partial differential equations en
ΔημιουργόςPatera, Adolf, 1836-1912en
ΔημιουργόςRovas Dimitriosen
ΔημιουργόςΡοβας Δημητριοςel
ΔημιουργόςC. Prud’hommeen
ΔημιουργόςVeroy, Karenen
ΕκδότηςAmerican Institute of Aeronautics and Astronauticsen
ΠερίληψηWe present a technique for the rapid and reliable prediction of linear–functional out- puts of elliptic partial differential equations with affine parameter dependence. The essential components are (i) rapidly convergent global reduced–basis approximations — (Galerkin) projection onto a space WN spanned by solutions of the governing partial dif- ferential equation at N selected points in parameter space; (ii) a posteriori error estimation — relaxations of the error-residual equation that provide inexpensive yet sharp bounds for the error in the outputs of interest; and (iii) off-line/on-line computational procedures — methods which decouple the generation and projection stages of the approximation process. The operation count for the on–line stage — in which, given a new parameter value, we calculate the output of interest and associated error bound — depends only on N (typically very small) and the parametric complexity of the problem. In this paper we develop new a posteriori error estimation procedures for noncoercive linear, and certain nonlinear, problems that yield rigorous and sharp error statements for all N. We consider three particular examples: the Helmholtz (reduced-wave) equation; a cubically nonlinear Poisson equation; and Burgers equation — a model for incompressible Navier-Stokes. The Helmholtz (and Burgers) example introduce our new lower bound constructions for the requisite inf-sup (singular value) stability factor; the cubic nonlin- earity exercises symmetry factorization procedures necessary for treatment of high-order Galerkin summations in the (say) residual dual-norm calculation; and the Burgers equa- tion illustrates our accommodation of potentially multiple solution branches in our a posteriori error statement. Numerical results are presented that demonstrate the rigor, sharpness, and efficiency of our proposed error bounds, and the application of these bounds to adaptive (optimal) approximation.en
ΤύποςΑφίσα σε Συνέδριοel
ΤύποςConference Posteren
Άδεια Χρήσηςhttp://creativecommons.org/licenses/by/4.0/en
Ημερομηνία2015-10-17-
Ημερομηνία Δημοσίευσης2003-
Θεματική ΚατηγορίαGreek mathematicsen
Θεματική Κατηγορίαmathematics greeken
Θεματική Κατηγορίαgreek mathematicsen
Θεματική ΚατηγορίαHelmholtz equationen
Βιβλιογραφική ΑναφοράK. Veroy, C. Prud’homme, D.V. Rovas, A.T. Patera.(2003).A posteriori error bounds for reduced-basis approximation of parametrized noncoercive and nonlinear elliptic partial differential equations.Presented at f the 16th AIAA computational fluid dynamics conference .[online].Available:http://augustine.mit.edu/methodology/papers/atpAIAA2003.pdfen

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