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Certified reduced-basis solutions of viscous Burgers equationparametrized by initial and boundary values

Published online by Cambridge University Press:  11 January 2013

Alexandre Janon ,
Maëlle Nodet  and
Clémentine Prieur
Alexandre Janon
Affiliation:
Joseph Fourier University, LJK/MOISE, BP 53, 38041 Grenoble Cedex, France.. alexandre.janon@imag.fr; maelle.nodet@inria.fr; clementine.prieur@imag.fr .
Maëlle Nodet
Affiliation:
Joseph Fourier University, LJK/MOISE, BP 53, 38041 Grenoble Cedex, France.. alexandre.janon@imag.fr; maelle.nodet@inria.fr; clementine.prieur@imag.fr .
Clémentine Prieur
Affiliation:
Joseph Fourier University, LJK/MOISE, BP 53, 38041 Grenoble Cedex, France.. alexandre.janon@imag.fr; maelle.nodet@inria.fr; clementine.prieur@imag.fr .
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Abstract

We present a reduced basis offline/online procedure for viscous Burgers initial boundaryvalue problem, enabling efficient approximate computation of the solutions of thisequation for parametrized viscosity and initial and boundary value data. This procedurecomes with a fast-evaluated rigorous error bound certifying the approximation procedure.Our numerical experiments show significant computational savings, as well as efficiency ofthe error bound.

Keywords

Reduced-basis methodsparametrized PDEsnonlinear PDEsBurgers equation
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 47 , Issue 2 , March 2013 , pp. 317 - 348
Copyright
© EDP Sciences, SMAI, 2013

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