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- Marianne Bessemoulin-Chatard, Francis Filbet
- SIAM J. Scientific Computing
- 2002

We propose a second order finite volume scheme for nonlinear degenerate parabolic equations. For some of these models (porous media equation, drift-diffusion system for semiconductors, ...) it has been proved that the transient solution converges to a steady-state when time goes to infinity. The present scheme preserves steady-states and provides a… (More)

- Marianne Bessemoulin-Chatard
- Numerische Mathematik
- 2012

Abstract We propose a finite volume scheme for convection-diffusion equations with nonlinear diffusion. Such equations arise in numerous physical contexts. We will particularly focus on the drift-diffusion system for semiconductors and the porous media equation. In these two cases, it is shown that the transient solution converges to a steady-state solution… (More)

We prove several discrete Gagliardo-Nirenberg-Sobolev and Poincaré-Sobolev inequalities for some approximations with arbitrary boundary values on finite volume meshes. The keypoint of our approach is to use the continuous embedding of the space BV (Ω) into L (Ω) for a Lipschitz domain Ω ⊂ R , with N ≥ 2. Finally, we give several applications to discrete… (More)

We define a combined edge FV-FE scheme for a bone healing model. This choice of discretization allows to take into account anisotropic diffusions and does not impose any restrictions on the mesh. Moreover, following [3], we propose a nonlinear correction to obtain a monotone scheme. We present some numerical experiments which show its good behavior.

- Marianne Bessemoulin-Chatard, Claire Chainais-Hillairet, Marie Hélène Vignal
- SIAM J. Numerical Analysis
- 2014

In this paper, we are interested in the numerical approximation of the classical time-dependent drift-diffusion system near quasi-neutrality. We consider a fully implicit in time and finite volume in space scheme, where the convection-diffusion fluxes are approximated by ScharfetterGummel fluxes. We establish that all the a priori estimates needed to prove… (More)

- Marianne Bessemoulin-Chatard, Mazen Saad
- J. Computational Applied Mathematics
- 2017

In this article, we propose and analyse a combined finite volume–finite element scheme for a bone healing model. This choice of discretization allows to take into account anisotropic diffusions without imposing any restrictions on the mesh. Moreover, following the work of C. Cancès et al. 2013, we define a nonlinear correction of the diffusive terms to… (More)

In this paper, we study the large–time behavior of a numerical scheme discretizing drift– diffusion systems for semiconductors. The numerical method is finite volume in space, implicit in time, and the numerical fluxes are a generalization of the classical Scharfetter– Gummel scheme which allows to consider both linear or nonlinear pressure laws. We study… (More)

A finite volume scheme for the (Patlak-) Keller-Segel model in two space dimensions with an additional cross-diffusion term in the elliptic equation for the chemical signal is analyzed. The main feature of the model is that there exists a new entropy functional yielding gradient estimates for the cell density and chemical concentration. The main features of… (More)

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