The Upwind Source at Interface (U.S.I.) method for hyperbolic conservation laws with source term introduced by Perthame and Simeoni is essentially first order accurate. Under appropriate hypotheses of consistency on the finite volume discretization of the source term, we prove L p-error estimates , 1 ≤ p <+∞, in the case of a uniform spatial mesh, for which… (More)
We develop a quantitative criterion determining the onset of localization and shear band formation at high-strain rate deformations of metals. We introduce an asymptotic procedure motivated by the theory of relaxation and the Chapman-Enskog expansion and derive an effective equation for the evolution of the strain rate, consisting of a second-order… (More)
Hyperbolic conservation laws with source terms arise in many applications, especially as a model for geophysical flows because of the gravity, and their numerical approximation leads to specific difficulties. In the context of finite volume schemes, many authors have proposed to Upwind Sources at Interfaces, i.e. the " U. S. I. " method, while a… (More)
We consider finite volume relaxation schemes for multidimensional scalar conservation laws. These schemes are constructed by appropriate dis-cretization of a relaxation system and it is shown to converge to the entropy solution of the conservation law with a rate of h 1/4 in L ∞ ([0, T ], L 1 loc (R d)) .