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

Mária Lukáčová-Medviďová; Jitka Saibertová; Gerald G. Warnecke; Yousef Zahaykah

Applications of Mathematics (2004)

  • Volume: 49, Issue: 5, page 415-439
  • ISSN: 0862-7940

Abstract

top
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 experiments for both the Maxwell and the linearized Euler equations.

How to cite

top

Lukáčová-Medviďová, Mária, et al. "On evolution Galerkin methods for the Maxwell and the linearized Euler equations." Applications of Mathematics 49.5 (2004): 415-439. <http://eudml.org/doc/33193>.

@article{Lukáčová2004,
abstract = {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 experiments for both the Maxwell and the linearized Euler equations.},
author = {Lukáčová-Medviďová, Mária, Saibertová, Jitka, Warnecke, Gerald G., Zahaykah, Yousef},
journal = {Applications of Mathematics},
keywords = {hyperbolic systems; wave equation; evolution Galerkin schemes; Maxwell equations; linearized Euler equations; divergence-free; vorticity; dispersion; hyperbolic systems; wave equation; evolution Galerkin schemes; Maxwell equations; divergence-free; vorticity; dispersion},
language = {eng},
number = {5},
pages = {415-439},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On evolution Galerkin methods for the Maxwell and the linearized Euler equations},
url = {http://eudml.org/doc/33193},
volume = {49},
year = {2004},
}

TY - JOUR
AU - Lukáčová-Medviďová, Mária
AU - Saibertová, Jitka
AU - Warnecke, Gerald G.
AU - Zahaykah, Yousef
TI - On evolution Galerkin methods for the Maxwell and the linearized Euler equations
JO - Applications of Mathematics
PY - 2004
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 49
IS - 5
SP - 415
EP - 439
AB - 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 experiments for both the Maxwell and the linearized Euler equations.
LA - eng
KW - hyperbolic systems; wave equation; evolution Galerkin schemes; Maxwell equations; linearized Euler equations; divergence-free; vorticity; dispersion; hyperbolic systems; wave equation; evolution Galerkin schemes; Maxwell equations; divergence-free; vorticity; dispersion
UR - http://eudml.org/doc/33193
ER -

References

top
  1. Advance Engineering Electromagnetics, John Wiley & Sons, New York-Chichester-Brisbane-Toronto-Singapore, 1989. (1989) 
  2. Field and Wave Electromagnetics, Addison-Wesley Publishing Company, second edition, 1989. (second edition, 1989) 
  3. Classical Electrodynamics, John Wiley & Sons, third edition, New York, 1999. (1999) Zbl0920.00012MR0436782
  4. 10.1002/fld.297, Internat. J. Numer. Methods Fluids 40 (2002), 425–434. (2002) MR1932992DOI10.1002/fld.297
  5. 10.1090/S0025-5718-00-01228-X, Math. Comp. 69 (2000), 1355–1348. (2000) MR1709154DOI10.1090/S0025-5718-00-01228-X
  6. 10.1006/jcph.2002.7207, J.  Comput. Phys. 183 (2002), 533–562. (2002) MR1947781DOI10.1006/jcph.2002.7207
  7. 10.1002/zamm.200310103, Z. Angew. Math. Mech. 84 (2004), 237–251. (2004) MR2045490DOI10.1002/zamm.200310103
  8. Third order finite volume evolution Galerkin (FVEG) methods for two-dimensional wave equation system, J. Numer. Math. 11 (2003), 235–251. (2003) MR2018817
  9. 10.1002/(SICI)1099-1476(19970910)20:13<1111::AID-MMA903>3.0.CO;2-1, Math. Methods Appl. Sci. 20 (1997), 1111–1125. (1997) MR1465396DOI10.1002/(SICI)1099-1476(19970910)20:13<1111::AID-MMA903>3.0.CO;2-1
  10. 10.1137/0705041, SIAM J. Numer. Anal. 5 (1968), 506–517. (1968) MR0235754DOI10.1137/0705041
  11. Evolution Galerkin schemes and discrete boundary condition for multidimensional first order systems, PhD.  thesis, Magdeburg, 2002. (2002) 

NotesEmbed ?

top

You must be logged in to post comments.