Add to ORKGWe construct a solution to a 2 × 2 strictly hyperbolic system of conservation laws, showing that the Godunov scheme [12] can produce an arbitrarily large amount of oscillations. This happens when the speed of a shock is close to rational, inducing a resonance with the grid. Differently from the Glimm scheme or the vanishing viscosity method, for systems of conservation laws our counterexample indicates that no a priori BV bounds or L1 stability estimates can in general be valid for finite difference schemes.
This paper is concerned with the numerical approximation of Cauchy problems for one-dimensional nonc...
We tackle, using the Isothermal Gas Equations, the problem of loss of monotonicity behind slowly mov...
Consider a strictly hyperbolic n x n system of conservation laws in one space dimension: ut+f(u)x=0...
We are interested in the numerical resolution of hyperbolic systems of conservation laws which don&a...
We study long time behavior of the solutions of the Godunov scheme to hyperbolic systems of conserva...
Hyperbolic systems of partial differential equations with relaxation source terms arise in the model...
International audienceWe present in this paper a new approximate Godunov solver called WFRoe which a...
In this paper, we developed a Godunov scheme for solving nonconservative systems. The main idea of ...
In this paper we are going to study the gas evolution dynamics of the exact and approximate Riemann ...
Abstract. In this short paper, we recall some well-known results on hyperbolic systems of conservati...
Abstract. In this short paper, we recall some well known results on hyper-bolic systems of conservat...
This paper identifies a new pathology that can be found for numerical simulations of nonlinear conse...
International audienceWe study hyperbolic systems of conservation laws in one space variable, in par...
Through a linear analysis, we show how to modify Godunov type schemes applied to the compressible Eu...
In this paper we study the asymptotic nonlinear stability of discrete shocks for the Lax-Friedrichs ...
This paper is concerned with the numerical approximation of Cauchy problems for one-dimensional nonc...
We tackle, using the Isothermal Gas Equations, the problem of loss of monotonicity behind slowly mov...
Consider a strictly hyperbolic n x n system of conservation laws in one space dimension: ut+f(u)x=0...
We are interested in the numerical resolution of hyperbolic systems of conservation laws which don&a...
We study long time behavior of the solutions of the Godunov scheme to hyperbolic systems of conserva...
Hyperbolic systems of partial differential equations with relaxation source terms arise in the model...
International audienceWe present in this paper a new approximate Godunov solver called WFRoe which a...
In this paper, we developed a Godunov scheme for solving nonconservative systems. The main idea of ...
In this paper we are going to study the gas evolution dynamics of the exact and approximate Riemann ...
Abstract. In this short paper, we recall some well-known results on hyperbolic systems of conservati...
Abstract. In this short paper, we recall some well known results on hyper-bolic systems of conservat...
This paper identifies a new pathology that can be found for numerical simulations of nonlinear conse...
International audienceWe study hyperbolic systems of conservation laws in one space variable, in par...
Through a linear analysis, we show how to modify Godunov type schemes applied to the compressible Eu...
In this paper we study the asymptotic nonlinear stability of discrete shocks for the Lax-Friedrichs ...
This paper is concerned with the numerical approximation of Cauchy problems for one-dimensional nonc...
We tackle, using the Isothermal Gas Equations, the problem of loss of monotonicity behind slowly mov...
Consider a strictly hyperbolic n x n system of conservation laws in one space dimension: ut+f(u)x=0...