Convergence of a streamline diffusion finite element method for scalar conservation laws with boundary conditions
Convergence of approximate solutions of a differential equation
Convergence of approximate solutions to scalar conservation laws by degenerate diffusion
Convergence of finite difference schemes for viscous and inviscid conservation laws with rough coefficients
We consider the initial value problem for degenerate viscous and inviscid scalar conservation laws where the flux function depends on the spatial location through a “rough” coefficient function . We show that the Engquist-Osher (and hence all monotone) finite difference approximations converge to the unique entropy solution of the governing equation if, among other demands, is in , thereby providing alternative (new) existence proofs for entropy solutions of degenerate convection-diffusion equations...
Convergence of finite difference schemes for viscous and inviscid conservation laws with rough coefficients
We consider the initial value problem for degenerate viscous and inviscid scalar conservation laws where the flux function depends on the spatial location through a "rough"coefficient function k(x). We show that the Engquist-Osher (and hence all monotone) finite difference approximations converge to the unique entropy solution of the governing equation if, among other demands, k' is in BV, thereby providing alternative (new) existence proofs for entropy solutions of degenerate convection-diffusion...
Convergence of implicit Finite Volume methods for scalar conservation laws with discontinuous flux function
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 [J. Evol. Eq. 3 (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...
Convergent finite element discretizations of the Navier-Stokes-Nernst-Planck-Poisson system
We propose and analyse two convergent fully discrete schemes to solve the incompressible Navier-Stokes-Nernst-Planck-Poisson system. The first scheme converges to weak solutions satisfying an energy and an entropy dissipation law. The second scheme uses Chorin's projection method to obtain an efficient approximation that converges to strong solutions at optimal rates.
Decay of positive waves in nonlinear systems of conservation laws
Description of the multi-dimensional finite volume solver EULER
This paper is aimed at the description of the multi-dimensional finite volume solver EULER, which has been developed for the numerical solution of the compressible Euler equations during several last years. The present overview of numerical schemes and the explanation of numerical techniques and tricks which have been used for EULER could be of certain interest not only for registered users but also for numerical mathematicians who have decided to implement a finite volume solver themselves. This...
Direct approach to mean-curvature flow with topological changes
This contribution deals with the numerical simulation of dislocation dynamics. Dislocations are described by means of the evolution of a family of closed or open smooth curves , . The curves are driven by the normal velocity which is the function of curvature and the position. The evolution law reads as: . The motion law is treated using direct approach numerically solved by two schemes, i. e., backward Euler semi-implicit and semi-discrete method of lines. Numerical stability is improved...
Dirichlet problem for a nonlinear conservation law.
In this paper we propose the study of a first-order non-linear hyperbolic equation in a bounded domain. We give a result of existence and uniqueness of the entropic measure-valued solution and of the entropic weak solution; for some general assumptions on the data.
Discontinuous solutions of the Cauchy problems for a scalar equation in nonconservative form
Entropy conditions and their numerical analogues for conservation laws
Entropy consistent, TVD methods with high accuracy for conservation laws.
Entropy production in second-order three-point schemes.
Équations de moment et conditions d'entropie pour des modèles cinétiques
Error estimates for scalar conservation laws by a kinetic approach.
Euler characteristic Galerkin scheme with recovery
Exact traveling wave solutions for discrete conservation laws.
Existence de lois de conservation dans le cas cyclique