no. 6
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.

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.

DOI : 10.1051/m2an/2014017
Classification : 35L45, 35L60, 35L65, 35L67
Mots clés : conservation laws, discontinuous flux, Lax−Friedrichs scheme, singular mapping, interface entropy condition, (A, b)connection 
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     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://www.numdam.org/articles/10.1051/m2an/2014017/}
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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://www.numdam.org/articles/10.1051/m2an/2014017/

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