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.
Mots-clés : reduced-basis methods, parametrized pdes, nonlinear PDEs, Burgers equation
@article{M2AN_2013__47_2_317_0,
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 },
pages = {317--348},
publisher = {EDP-Sciences},
volume = {47},
number = {2},
year = {2013},
doi = {10.1051/m2an/2012029},
mrnumber = {3021689},
zbl = {1272.35016},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2012029/}
}
TY - JOUR AU - Janon, Alexandre AU - Nodet, Maëlle AU - Prieur, Clémentine TI - Certified reduced-basis solutions of viscous Burgers equation parametrized by initial and boundary values JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2013 SP - 317 EP - 348 VL - 47 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2012029/ DO - 10.1051/m2an/2012029 LA - en ID - M2AN_2013__47_2_317_0 ER -
%0 Journal Article %A Janon, Alexandre %A Nodet, Maëlle %A Prieur, Clémentine %T Certified reduced-basis solutions of viscous Burgers equation parametrized by initial and boundary values %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2013 %P 317-348 %V 47 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2012029/ %R 10.1051/m2an/2012029 %G en %F M2AN_2013__47_2_317_0
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 , Tome 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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