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

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 similar to 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.