Displaying similar documents to “Diffusion limit of the Lorentz model : asymptotic preserving schemes”

On evolution Galerkin methods for the Maxwell and the linearized Euler equations

Mária Lukáčová-Medviďová, Jitka Saibertová, Gerald G. Warnecke, Yousef Zahaykah (2004)

Applications of Mathematics

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The subject of the paper is the derivation and analysis of evolution Galerkin schemes for the two dimensional Maxwell and linearized Euler equations. The aim is to construct a method which takes into account better the infinitely many directions of propagation of waves. To do this the initial function is evolved using the characteristic cone and then projected onto a finite element space. We derive the divergence-free property and estimate the dispersion relation as well. We present...

Finite volume schemes for multi-dimensional hyperbolic systems based on the use of bicharacteristics

Mária Lukáčová-Medviďová, Jitka Saibertová (2006)

Applications of Mathematics

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In this paper we present recent results for the bicharacteristic based finite volume schemes, the so-called finite volume evolution Galerkin (FVEG) schemes. These methods were proposed to solve multi-dimensional hyperbolic conservation laws. They combine the usually conflicting design objectives of using the conservation form and following the characteristics, or bicharacteristics. This is realized by combining the finite volume formulation with approximate evolution operators, which...

Transport of pollutant in shallow water : a two time steps kinetic method

Emmanuel Audusse, Marie-Odile Bristeau (2003)

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

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The aim of this paper is to present a finite volume kinetic method to compute the transport of a passive pollutant by a flow modeled by the shallow water equations using a new time discretization that allows large time steps for the pollutant computation. For the hydrodynamic part the kinetic solver ensures – even in the case of a non flat bottom – the preservation of the steady state of a lake at rest, the non-negativity of the water height and the existence of an entropy inequality....