AVERAGED MULTIVALUED SOLUTIONS FOR SCALAR CONSERVATION-LAWS

A time discretization is introduced for scalar conservation laws, which consists in averaging (in an appropriate sense) the generally multivalued solution given by the classical method of characteristics. Convergence toward the physical solutions satisfying the entropy condition is proved. Several numerical schemes are deduced after a full discretization, either with respect to the space variable (various known schemes are then recognized), or with respect to the phase variable (which leads to a space grid free scheme. ) Generalizations are considered toward systems of conservation laws and bidimensional scalar conservation laws.