In this paper we present a new reduced basis technique for parametrized nonlinear scalar conservation laws in presence of shocks. The essential ingredients are an efficient algorithm to approximate the shock curve, a procedure to detect the smooth components of the solution at the two sides of the shock, and a suitable interpolation strategy to reconstruct such smooth components during the online stage. The approach we propose is based on some theoretical properties of the solution to the problem. Some numerical examples prove the effectiveness of the proposed strategy.
DOI : 10.1051/m2an/2014054
Mots clés : Nonlinear conservation laws, model reduction, reduced basis method
@article{M2AN_2015__49_3_787_0, author = {Taddei, T. and Perotto, S. and Quarteroni, A.}, title = {Reduced basis techniques for nonlinear conservation laws}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {787--814}, publisher = {EDP-Sciences}, volume = {49}, number = {3}, year = {2015}, doi = {10.1051/m2an/2014054}, zbl = {1316.65079}, mrnumber = {3342228}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2014054/} }
TY - JOUR AU - Taddei, T. AU - Perotto, S. AU - Quarteroni, A. TI - Reduced basis techniques for nonlinear conservation laws JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2015 SP - 787 EP - 814 VL - 49 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2014054/ DO - 10.1051/m2an/2014054 LA - en ID - M2AN_2015__49_3_787_0 ER -
%0 Journal Article %A Taddei, T. %A Perotto, S. %A Quarteroni, A. %T Reduced basis techniques for nonlinear conservation laws %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2015 %P 787-814 %V 49 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2014054/ %R 10.1051/m2an/2014054 %G en %F M2AN_2015__49_3_787_0
Taddei, T.; Perotto, S.; Quarteroni, A. Reduced basis techniques for nonlinear conservation laws. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 49 (2015) no. 3, pp. 787-814. doi : 10.1051/m2an/2014054. http://www.numdam.org/articles/10.1051/m2an/2014054/
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