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

Adimurthi; Rajib Dutta; G. D. Veerappa Gowda; Jérôme Jaffré

- Volume: 48, Issue: 6, page 1725-1755
- ISSN: 0764-583X

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topAdimurthi, et al. "Monotone (A,B) entropy stable numerical scheme for Scalar Conservation Laws with discontinuous flux." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 48.6 (2014): 1725-1755. <http://eudml.org/doc/273304>.

@article{Adimurthi2014,

abstract = {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.},

author = {Adimurthi, Dutta, Rajib, Veerappa Gowda, G. D., Jaffré, Jérôme},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {conservation laws; discontinuous flux; Lax−Friedrichs scheme; singular mapping; interface entropy condition; (A; b)connection; connection; Lax-Friedrichs scheme; stability; convergece},

language = {eng},

number = {6},

pages = {1725-1755},

publisher = {EDP-Sciences},

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

url = {http://eudml.org/doc/273304},

volume = {48},

year = {2014},

}

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 - Modélisation Mathématique et Analyse Numérique

PY - 2014

PB - EDP-Sciences

VL - 48

IS - 6

SP - 1725

EP - 1755

AB - 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.

LA - eng

KW - conservation laws; discontinuous flux; Lax−Friedrichs scheme; singular mapping; interface entropy condition; (A; b)connection; connection; Lax-Friedrichs scheme; stability; convergece

UR - http://eudml.org/doc/273304

ER -

## References

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