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On Evolution Galerkin Methods for the Maxwell and the Linearized Euler Equations

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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.

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Authors and Affiliations

  1. Arbeitsbereich Mathematik, Technische Universität Hamburg-Harburg, Schwarzenbergstraße 95, 21 073, Hamburg, Germany

    Mária Lukáčová-Medviďová

  2. Department of Mathematics, Faculty of Mechanical Engineering, University of Technology Brno, Technická 2, 616 39, Brno, Czech Republic

    Mária Lukáčová-Medviďová & Jitka Saibertová

  3. Institut für Analysis und Numerik, Ottovon-Guericke-Universität Magdeburg, Universitätsplatz 2, 39 106, Magdeburg, Germany

    Gerald Warnecke & Yousef Zahaykah

Authors
  1. Mária Lukáčová-Medviďová
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  2. Jitka Saibertová
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  3. Gerald Warnecke
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  4. Yousef Zahaykah
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Lukáčová-Medviďová, M., Saibertová, J., Warnecke, G. et al. On Evolution Galerkin Methods for the Maxwell and the Linearized Euler Equations. Applications of Mathematics 49, 415–439 (2004). https://doi.org/10.1023/B:APOM.0000048121.68355.2a

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  • DOI: https://doi.org/10.1023/B:APOM.0000048121.68355.2a

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