Claire Chainais-Hillairet

FINITE VOLUME APPROXIMATION FOR DEGENERATE DRIFT-DIFFUSION SYSTEM IN SEVERAL SPACE DIMENSIONS

This paper is devoted to a finite volume discretization for multidimensional nonlinear drift-diffusion system. Such system arises in semiconductors modelling and is composed of two degenerate parabolic equations and an elliptic one. We prove the convergence of the finite volume scheme and then the existence of solutions to the problem. Several numerical tests show the efficiency of the method.

Convergence Analysis of a Mixed Finite Volume Scheme for an Elliptic-Parabolic System Modeling Miscible Fluid Flows in Porous Media

We study a finite volume discretization of a strongly coupled elliptic-parabolic PDE system describing miscible displacement in a porous medium. We discretize each equation by a finite volume scheme which allows a wide variety of unstructured grids (in any space dimension) and gives strong enough convergence for handling the nonlinear coupling of the equations. We prove the convergence of the scheme as the time and space steps go to

Numerical methods for the simulation of a corrosion model with moving oxide layer

0

Finite volume schemes for nonhomogeneous scalar conservation laws: error estimate

. Finally, we provide numerical results to demonstrate the efficiency of the proposed numerical scheme.

Mathematical and numerical study of a corrosion model

In this paper, we design numerical methods for a PDE system arising in corrosion modeling. This system describes the evolution of a dense oxide layer. It is based on a drift-diffusion system and includes moving boundary equations. The choice of the numerical methods is justified by a stability analysis and by the study of their numerical performance. Finally, numerical experiments with real-life data shows the efficiency of the developed methods.

Study of a Finite Volume Scheme for the Drift-Diffusion System. Asymptotic Behavior in the Quasi-Neutral Limit

Summary. In this paper, we study finite volume schemes for the nonhomogeneous scalar conservation law

Entropy Method and Asymptotic Behaviours of Finite Volume Schemes

u_t +{\rm div} F(x,t,u)=q(x,t,u)

Exponential decay of a finite volume scheme to the thermal equilibrium for drift–diffusion systems

with initial condition

Study of Discrete Duality Finite Volume Schemes for the Peaceman Model

u(x,0)=\u0(x)

Convergence of a Finite Volume Scheme for a Corrosion Model

. The source term may be either stiff or nonstiff. In both cases, we prove error estimates between the approximate solution given by a finite volume scheme (the scheme is totally explicit in the nonstiff case, semi-implicit in the stiff case) and the entropy solution. The order of these estimates is