For scalar conservation laws in one space dimension with a flux function discontinuous in space, there exist infinitely many classes of solutions which are L1 contractive. Each class is characterized by a connection (A,B) which determines the interface entropy. For solutions corresponding to a connection (A,B), there exists convergent numerical schemes based on Godunov or Engquist-Osher schemes. The natural question is how to obtain schemes, corresponding to computationally less expensive monotone schemes like Lax-Friedrichs etc., used widely in applications. In this paper we completely answer this question for more general (A,B) stable monotone schemes using a novel construction of interface flux function. Then from the singular mapping technique of Temple and chain estimate of Adimurthi and Gowda, we prove the convergence of the schemes.
Mots-clés : conservation laws, discontinuous flux, Lax−Friedrichs scheme, singular mapping, interface entropy condition, (A, b)connection
@article{M2AN_2014__48_6_1725_0, author = {Adimurthi and Dutta, Rajib and Veerappa Gowda, G. D. and Jaffr\'e, J\'er\^ome}, title = {Monotone $(A,B)$ entropy stable numerical scheme for {Scalar} {Conservation} {Laws} with discontinuous flux}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {1725--1755}, publisher = {EDP-Sciences}, volume = {48}, number = {6}, year = {2014}, doi = {10.1051/m2an/2014017}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/m2an/2014017/} }
TY - JOUR AU - Adimurthi AU - Dutta, Rajib AU - Veerappa Gowda, G. D. AU - Jaffré, Jérôme TI - Monotone $(A,B)$ entropy stable numerical scheme for Scalar Conservation Laws with discontinuous flux JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2014 SP - 1725 EP - 1755 VL - 48 IS - 6 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an/2014017/ DO - 10.1051/m2an/2014017 LA - en ID - M2AN_2014__48_6_1725_0 ER -
%0 Journal Article %A Adimurthi %A Dutta, Rajib %A Veerappa Gowda, G. D. %A Jaffré, Jérôme %T Monotone $(A,B)$ entropy stable numerical scheme for Scalar Conservation Laws with discontinuous flux %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2014 %P 1725-1755 %V 48 %N 6 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an/2014017/ %R 10.1051/m2an/2014017 %G en %F M2AN_2014__48_6_1725_0
Adimurthi; Dutta, Rajib; Veerappa Gowda, G. D.; Jaffré, Jérôme. Monotone $(A,B)$ entropy stable numerical scheme for Scalar Conservation Laws with discontinuous flux. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 48 (2014) no. 6, pp. 1725-1755. doi : 10.1051/m2an/2014017. http://archive.numdam.org/articles/10.1051/m2an/2014017/
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