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Convergence of locally divergence-free discontinuous-Galerkin methods for the induction equations of the 2D-MHD system

Published online by Cambridge University Press:  15 November 2005

Nicolas Besse  and
Dietmar Kröner
Nicolas Besse
Affiliation:
Institut de Recherche Mathematique Avancée, Université Louis Pasteur, CNRS, 7 rue René Descartes, 67084 Strasbourg Cedex, France. besse@math.u-strasbg.fr
Dietmar Kröner
Affiliation:
Institut für Angewandte Mathematik Universität Freiburg, Hermann-Herder-Str. 10, 79104 Freiburg i. Br., Germany. dietmar@mathematik.uni-freiburg.de
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Abstract

We present the convergence analysis of locally divergence-free discontinuous Galerkin methodsfor the induction equations which appear in the ideal magnetohydrodynamic system. When we use a second order Runge Kutta time discretization, under the CFL condition $\Delta t\sim h^{4/3}$ , we obtain error estimates in L 2 of order $\mathcal{O} (\Delta t^2 + h^{m + 1/2})$ where m is the degree of the local polynomials.

Keywords

Magnetohydrodynamicsdiscontinuous-Galerkin methodsconvergence analysis.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 39 , Issue 6 , November 2005 , pp. 1177 - 1202
Copyright
© EDP Sciences, SMAI, 2005

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