Geodesic
Finite volume schemes for multi-dimensional hyperbolic systems based on the use of bicharacteristics
Applications of Mathematics, Tome 51 (2006) no. 3, pp. 205-228.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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 of the multi-dimensional hyperbolic system. In this way all of the infinitely many directions of wave propagation are taken into account. The main goal of this paper is to present a self-contained overview on the recent results. We study the $L^1$-stability of the finite volume schemes obtained by various approximations of the flux integrals. Several numerical experiments presented in the last section confirm robustness and correct multi-dimensional behaviour of the FVEG methods.
DOI : 10.1007/s10492-006-0012-z
Classification : 35L45, 35L65, 65M12, 65M25, 65M60, 76M12
Keywords: multidimensional finite volume methods; bicharacteristics; hyperbolic systems; wave equation; Euler equations 
@article{10_1007_s10492_006_0012_z,
     author = {Luk\'a\v{c}ov\'a-Medvi\v{d}ov\'a, M\'aria and Saibertov\'a-Zato\v{c}ilov\'a, Jitka},
     title = {Finite volume schemes for multi-dimensional hyperbolic systems based on the use of bicharacteristics},
     journal = {Applications of Mathematics},
     pages = {205--228},
     publisher = {mathdoc},
     volume = {51},
     number = {3},
     year = {2006},
     doi = {10.1007/s10492-006-0012-z},
     mrnumber = {2228663},
     zbl = {1164.76358},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10492-006-0012-z/}
}
TY  - JOUR
AU  - Lukáčová-Medviďová, Mária
AU  - Saibertová-Zatočilová, Jitka
TI  - Finite volume schemes for multi-dimensional hyperbolic systems based on the use of bicharacteristics
JO  - Applications of Mathematics
PY  - 2006
SP  - 205
EP  - 228
VL  - 51
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10492-006-0012-z/
DO  - 10.1007/s10492-006-0012-z
LA  - en
ID  - 10_1007_s10492_006_0012_z
ER  - 
%0 Journal Article
%A Lukáčová-Medviďová, Mária
%A Saibertová-Zatočilová, Jitka
%T Finite volume schemes for multi-dimensional hyperbolic systems based on the use of bicharacteristics
%J Applications of Mathematics
%D 2006
%P 205-228
%V 51
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1007/s10492-006-0012-z/
%R 10.1007/s10492-006-0012-z
%G en
%F 10_1007_s10492_006_0012_z
Lukáčová-Medviďová, Mária; Saibertová-Zatočilová, Jitka. Finite volume schemes for multi-dimensional hyperbolic systems based on the use of bicharacteristics. Applications of Mathematics, Tome 51 (2006) no. 3, pp. 205-228. doi : 10.1007/s10492-006-0012-z. http://geodesic.mathdoc.fr/articles/10.1007/s10492-006-0012-z/

Cité par Sources :