Certified reduced-basis solutions of viscous Burgers equation parametrized by initial and boundary values
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 47 (2013) no. 2, pp. 317-348.

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.

DOI: 10.1051/m2an/2012029
Classification: 35K20,  35K55,  65M15,  65M60
Keywords: reduced-basis methods, parametrized pdes, nonlinear PDEs, Burgers equation
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     author = {Janon, Alexandre and Nodet, Ma\"elle and Prieur, Cl\'ementine},
     title = {Certified reduced-basis solutions of viscous {Burgers} equation parametrized by initial and boundary values},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     pages = {317--348},
     publisher = {EDP-Sciences},
     volume = {47},
     number = {2},
     year = {2013},
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Janon, Alexandre; Nodet, Maëlle; Prieur, Clémentine. Certified reduced-basis solutions of viscous Burgers equation parametrized by initial and boundary values. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 47 (2013) no. 2, pp. 317-348. doi : 10.1051/m2an/2012029. http://www.numdam.org/articles/10.1051/m2an/2012029/

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