Displaying similar documents to “A first order accuracy scheme on non-uniform mesh.”

Resolution of the time dependent equations by a Godunov type scheme having the diffusion limit

Patricia Cargo, Gérald Samba (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We consider the model to approximate the time dependent transport equation in one dimension of space. In a diffusive regime, the solution of this system is solution of a diffusion equation. We are looking for a numerical scheme having the diffusion limit property: in a diffusive regime, it has to give the solution of the limiting diffusion equation on a mesh at the diffusion scale. The numerical scheme proposed is an extension of the Godunov type scheme proposed by...

Necessary conditions for uniform convergence of finite difference schemes for convection-diffusion problems with exponential and parabolic layers

Hans-Görg Roos, Martin Stynes (1996)

Applications of Mathematics

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Singularly perturbed problems of convection-diffusion type cannot be solved numerically in a completely satisfactory manner by standard numerical methods. This indicates the need for robust or ϵ -uniform methods. In this paper we derive new conditions for such schemes with special emphasize to parabolic layers.