Displaying similar documents to “Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis”

Small-stencil 3D schemes for diffusive flows in porous media

Robert Eymard, Cindy Guichard, Raphaèle Herbin (2012)

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

Similarity:

In this paper, we study some discretization schemes for diffusive flows in heterogeneous anisotropic porous media. We first introduce the notion of gradient scheme, and show that several existing schemes fall into this framework. Then, we construct two new gradient schemes which have the advantage of a small stencil. Numerical results obtained for real reservoir meshes show the efficiency of the new schemes, compared to existing ones.

A linear scheme to approximate nonlinear cross-diffusion systems

Hideki Murakawa (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

Similarity:

This paper proposes a linear discrete-time scheme for general nonlinear cross-diffusion systems. The scheme can be regarded as an extension of a linear scheme based on the nonlinear Chernoff formula for the degenerate parabolic equations, which proposed by Berger [ (1979) 297–312]. We analyze stability and convergence of the linear scheme. To this end, we apply the theory of reaction-diffusion system approximation. After discretizing the scheme in space, we obtain a...