Averaged multivalued solutions for scalar conservation laws. (English) Zbl 0565.65054

Brenier, Yann

SIAM J. Numer. Anal. 21, 1013-1037 (1984).

A time discretization for scalar conservation laws which consists in averaging the generally multivalued solution constructed by the classical method of characteristics is proposed and its convergence toward the solution satisfying the entropy condition is proved. On this base several numerical schemes are deduced and some generalizations toward systems of conservation laws and bidimensional scalar conservation laws are considered.

Reviewer: V.Kostova

MSC:

65M25	Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs
35L65	Hyperbolic conservation laws

Keywords:

averaged multivalued solutions; time discretization; convergence; entropy condition

Software:

HLLE