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

Besse, Nicolas; Kröner, Dietmar

ESAIM: Modélisation mathématique et analyse numérique, Tome 39 (2005) no. 6, pp. 1177-1202.

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 $𝒪(\Delta t^2+h^{m+1/2})$ where $m$ is the degree of the local polynomials.

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