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

Mária Lukáčová-Medviďová;  Jitka Saibertová — 2006

Applications of Mathematics

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 use bicharacteristics...

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

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 some numerical...

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