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

Besse, Nicolas ; Kröner, Dietmar

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 39 (2005), p. 1177-1202 / Harvested from Numdam

Résumé

We present the convergence analysis of locally divergence-free discontinuous Galerkin methods for 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.

Détail

Publié le : 2005-01-01

MR 2195909 | Zbl 1084.76046 | 1 citation dans Numdam

DOI : https://doi.org/10.1051/m2an:2005051
Classification:  76W05,  65J10

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