Monotone (A,B) entropy stable numerical scheme for Scalar Conservation Laws with discontinuous flux
1 TIFR-CAM, PB 6503,
firstname.lastname@example.org; email@example.com; firstname.lastname@example.org
2 INRIA, BP 105, 78153 Le Chesnay Cedex, France.
Revised: 2 September 2013
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.
Mathematics Subject Classification: 35L45 / 35L60 / 35L65 / 35L67
Key words: Conservation laws / discontinuous flux / Lax−Friedrichs scheme / singular mapping / interface entropy condition / (A,B)connection
© EDP Sciences, SMAI, 2014