| Title:
|
On evolution Galerkin methods for the Maxwell and the linearized Euler equations (English) |
| Author:
|
Lukáčová-Medviďová, Mária |
| Author:
|
Saibertová, Jitka |
| Author:
|
Warnecke, Gerald |
| Author:
|
Zahaykah, Yousef |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
49 |
| Issue:
|
5 |
| Year:
|
2004 |
| Pages:
|
415-439 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
hyperbolic systems |
| Keyword:
|
wave equation |
| Keyword:
|
evolution Galerkin schemes |
| Keyword:
|
Maxwell equations |
| Keyword:
|
linearized Euler equations |
| Keyword:
|
divergence-free |
| Keyword:
|
vorticity |
| Keyword:
|
dispersion |
| MSC:
|
35A35 |
| MSC:
|
35Q35 |
| MSC:
|
35Q60 |
| MSC:
|
65M60 |
| MSC:
|
76B99 |
| MSC:
|
76M10 |
| MSC:
|
78M10 |
| idZBL:
|
Zbl 1099.65088 |
| idMR:
|
MR2086087 |
| DOI:
|
10.1023/B:APOM.0000048121.68355.2a |
| . |
| Date available:
|
2009-09-22T18:19:09Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134577 |
| . |
| Reference:
|
[1] C. A. Balanis: Advance Engineering Electromagnetics.John Wiley & Sons, New York-Chichester-Brisbane-Toronto-Singapore, 1989. |
| Reference:
|
[2] D. K. Cheng: Field and Wave Electromagnetics.Addison-Wesley Publishing Company, second edition, 1989. |
| Reference:
|
[3] J. D. Jackson: Classical Electrodynamics.John Wiley & Sons, third edition, New York, 1999. Zbl 0920.00012, MR 0436782 |
| Reference:
|
[4] M. Lukáčová-Medviďová, K. W. Morton, and G. Warnecke: Finite volume evolution, Galerkin metods for Euler equations of gas dynamics.Internat. J. Numer. Methods Fluids 40 (2002), 425–434. MR 1932992, 10.1002/fld.297 |
| Reference:
|
[5] M. Lukáčová-Medviďová, K. W. Morton, and G. Warnecke: Evolution Galerkin methods for hyperbolic systems in two space dimensions.Math. Comp. 69 (2000), 1355–1348. MR 1709154, 10.1090/S0025-5718-00-01228-X |
| Reference:
|
[6] M. Lukáčová-Medviďová, J. Saibertová, and G. Warnecke: Finite volume evolution Galerkin methods for nonlinear hyperbolic systems.J. Comput. Phys. 183 (2002), 533–562. MR 1947781, 10.1006/jcph.2002.7207 |
| Reference:
|
[7] M. Lukáčová-Medviďová, G. Warnecke, and Y. Zahaykah: On the boundary conditions for EG-methods applied to the two-dimensional wave equation system.Z. Angew. Math. Mech. 84 (2004), 237–251. MR 2045490, 10.1002/zamm.200310103 |
| Reference:
|
[8] M. Lukáčová-Medviďová, G. Warnecke, and Y. Zahaykah: Third order finite volume evolution Galerkin (FVEG) methods for two-dimensional wave equation system.J. Numer. Math. 11 (2003), 235–251. MR 2018817 |
| Reference:
|
[9] S. Ostkamp: Multidimensional characteristic Galerkin schemes and evolution operators for hyperbolic systems.Math. Methods Appl. Sci. 20 (1997), 1111–1125. MR 1465396, 10.1002/(SICI)1099-1476(19970910)20:13<1111::AID-MMA903>3.0.CO;2-1 |
| Reference:
|
[10] G. Strang: On the construction and comparison of difference schemes.SIAM J. Numer. Anal. 5 (1968), 506–517. MR 0235754, 10.1137/0705041 |
| Reference:
|
[11] Y. Zahaykah: Evolution Galerkin schemes and discrete boundary condition for multidimensional first order systems.PhD. thesis, Magdeburg, 2002. |
| . |
