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

Alexandre Janon 1, * Maëlle Nodet 1 Clémentine Prieur 1, 2
* Corresponding author
1 MOISE - Modelling, Observations, Identification for Environmental Sciences
Grenoble INP [2007-2019] - Institut polytechnique de Grenoble - Grenoble Institute of Technology [2007-2019], LJK [2007-2015] - Laboratoire Jean Kuntzmann [2007-2015], Inria Grenoble - Rhône-Alpes
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.
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Submitted on : Sunday, June 17, 2012 - 10:29:00 AM
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Alexandre Janon, Maëlle Nodet, Clémentine Prieur. Certified reduced-basis solutions of viscous Burgers equation parametrized by initial and boundary values. ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2013, 47 (2), pp.317-348. ⟨10.1051/m2an/2012029⟩. ⟨inria-00524727v2⟩

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