Displaying similar documents to “An efficient linear numerical scheme for the Stefan problem, the porous medium equation and nonlinear cross-diffusion systems”

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...

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...

Conservation schemes for convection-diffusion equations with Robin boundary conditions

Stéphane Flotron, Jacques Rappaz (2013)

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

Similarity:

In this article, we present a numerical scheme based on a finite element method in order to solve a time-dependent convection-diffusion equation problem and satisfy some conservation properties. In particular, our scheme is able to conserve the total energy for a heat equation or the total mass of a solute in a fluid for a concentration equation, even if the approximation of the velocity field is not completely divergence-free. We establish a priori errror estimates for this scheme and...

Nonlinear Tensor Diffusion in Image Processing

Stašová, Olga, Mikula, Karol, Handlovičová, Angela, Peyriéras, Nadine

Similarity:

This paper presents and summarize our results concerning the nonlinear tensor diffusion which enhances image structure coherence. The core of the paper comes from [3, 2, 4, 5]. First we briefly describe the diffusion model and provide its basic properties. Further we build a semi-implicit finite volume scheme for the above mentioned model with the help of a co-volume mesh. This strategy is well-known as diamond-cell method owing to the choice of co-volume as a diamondshaped polygon,...