Abstract
We consider the numerical solution of one-dimensional scalar conservation laws. In particular, we present some very simple, yet appropriate, discrete entropy fluxes for the class of fully-discrete E-schemes. We show that these provide the required entropy inequalities under sharp CFL conditions.
Similar content being viewed by others
References
Harten, A.: High resolution schemes for hyperbolic conservation laws. J. Comput. Phys. 49(3), 357–393 (1983)
Hopf, E.: On the right weak solution of the cauchy problem for a quasilinear equation of first order. J. Math. Mech. 19(6), 483–487 (1969)
Kružkov, S.N.: First order quasilinear equations in several independent variables. Math. USSR-Sb. 10(2), 217–243 (1970)
Lions, P.L., Perthame, B., Tadmor, E.: A kinetic formulation of multidimensional scalar conservation laws and related equations. J. Am. Math. Soc. 7(1), 169–191 (1994)
Makridakis, C., Perthame, B.: Sharp CFL, discrete kinetic formulation, and entropic schemes for scalar conservation laws. SIAM J. Numer. Anal. 41(3), 1032–1051 (2003)
Osher, S.: Riemann solvers, the entropy condition, and difference approximations. SIAM J. Numer. Anal. 21(2), 217–235 (1984)
Tadmor, E.: Numerical viscosity and the entropy condition for conservative difference schemes. Math. Comput. 43(168), 369–381 (1984)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.