Monotone (A,B) entropy stable numerical scheme for Scalar Conservation Laws with discontinuous flux

For scalar conservation laws in one space dimension with a flux function discontinuous in space, there exist infinitely many classes of solutions which are L 1 contractive. Each class is character- ized 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 EngquistOsher schemes. The natural question is how to obtain schemes, corresponding to computationally less expen- sive monotone schemes like LaxFriedrichs 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. 0(x)φ(x, 0)dx =0 . (1.3)