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

Autor:	Jérôme Jaffré, Rajib Dutta, G. D. Veerappa Gowda, Adimurthi
Rok vydání:	2014
Předmět:	Numerical Analysis Conservation law Applied Mathematics Existential quantification Mathematical analysis Space dimension Computational Mathematics Monotone polygon Mathematics Subject Classification Modeling and Simulation Applied mathematics Entropy (arrow of time) Analysis Mathematics
Zdroj:	ESAIM: Mathematical Modelling and Numerical Analysis. 48:1725-1755
ISSN:	1290-3841 0764-583X
Popis:	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)
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::bd59005560566fc0dc76934ba76aaea2 https://doi.org/10.1051/m2an/2014017 Zobrazit plný text záznamu