Geodesic
Reduced basis techniques for nonlinear conservation laws
Taddei, T.1  ; Perotto, S.2 ; Quarteroni, A.2, 3 
1 Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Ave, Rm. 3-237 Cambridge, MA 02139, USA.
2 MOX-Modeling and Scientific Computing, Dipartimento di Matematica “F. Brioschi”, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy.
3 Modelling and Scientific Computing, Institute of Analysis and Scientific Computing, École Polytechnique Féderale de Lausanne, Station 8, EPFL, 1015 Lausanne, Switzerland.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 49 (2015) no. 3, pp. 787-814

Voir la notice de l'article provenant de la source Numdam

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.

Reçu le :
DOI : 10.1051/m2an/2014054
Classification : 65M08, 65M15, 65M25, 35L65, 35L67
Keywords: Nonlinear conservation laws, model reduction, reduced basis method

Taddei, T. 1 ; Perotto, S. 2 ; Quarteroni, A. 2, 3

1 Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Ave, Rm. 3-237 Cambridge, MA 02139, USA.
2 MOX-Modeling and Scientific Computing, Dipartimento di Matematica “F. Brioschi”, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy.
3 Modelling and Scientific Computing, Institute of Analysis and Scientific Computing, École Polytechnique Féderale de Lausanne, Station 8, EPFL, 1015 Lausanne, Switzerland. 
@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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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

Cité par Sources :