Geodesic
On evolution Galerkin methods for the Maxwell and the linearized Euler equations
Applications of Mathematics, Tome 49 (2004) no. 5, pp. 415-439.

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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 some numerical experiments for both the Maxwell and the linearized Euler equations.
DOI : 10.1023/B:APOM.0000048121.68355.2a
Classification : 35A35, 35Q35, 35Q60, 65M60, 76B99, 76M10, 78M10
Keywords: hyperbolic systems; wave equation; evolution Galerkin schemes; Maxwell equations; linearized Euler equations; divergence-free; vorticity; dispersion 
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     author = {Luk\'a\v{c}ov\'a-Medvi\v{d}ov\'a, M\'aria and Saibertov\'a, Jitka and Warnecke, Gerald and Zahaykah, Yousef},
     title = {On evolution {Galerkin} methods for the {Maxwell} and the linearized {Euler} equations},
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Lukáčová-Medviďová, Mária; Saibertová, Jitka; Warnecke, Gerald; Zahaykah, Yousef. On evolution Galerkin methods for the Maxwell and the linearized Euler equations. Applications of Mathematics, Tome 49 (2004) no. 5, pp. 415-439. doi : 10.1023/B:APOM.0000048121.68355.2a. http://geodesic.mathdoc.fr/articles/10.1023/B:APOM.0000048121.68355.2a/

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