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Certified reduced-basis solutions of viscous Burgers equation parametrized 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 boundary value problem, enabling efficient approximate computation of the solutions of this equation for parametrized viscosity and initial and boundary value data. This procedure comes with a fast-evaluated rigorous error bound certifying the approximation procedure. Our numerical experiments show significant computational savings, as well as efficiency of the 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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