Displaying similar documents to “Convergence of finite difference schemes for viscous and inviscid conservation laws with rough coefficients”

Obstacle problems for scalar conservation laws

Laurent Levi (2001)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Similarity:

In this paper we are interested in bilateral obstacle problems for quasilinear scalar conservation laws associated with Dirichlet boundary conditions. Firstly, we provide a suitable entropy formulation which ensures uniqueness. Then, we justify the existence of a solution through the method of penalization and by referring to the notion of entropy process solution due to specific properties of bounded sequences in L ∞ . Lastly, we study the behaviour of this solution and its stability properties...

Numerical flux-splitting for a class of hyperbolic systems with unilateral constraint

Florent Berthelin (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Similarity:

We study in this paper some numerical schemes for hyperbolic systems with unilateral constraint. In particular, we deal with the scalar case, the isentropic gas dynamics system and the full-gas dynamics system. We prove the convergence of the scheme to an entropy solution of the isentropic gas dynamics with unilateral constraint on the density and mass loss. We also study the non-trivial steady states of the system.

Convergence of implicit Finite Volume methods for scalar conservation laws with discontinuous flux function

Sébastien Martin, Julien Vovelle (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

Similarity:

This paper deals with the problem of numerical approximation in the Cauchy-Dirichlet problem for a scalar conservation law with a flux function having finitely many discontinuities. The well-posedness of this problem was proved by Carrillo [  (2003) 687–705]. Classical numerical methods do not allow us to compute a numerical solution (due to the lack of regularity of the flux). Therefore, we propose an implicit Finite Volume method based on an equivalent formulation of the initial problem....