Stabilized discontinuous Galerkin scheme for the magnetic induction equation

Abstract

We design and analyze a discontinuous Galerkin scheme for the initial–boundary value problem associated with the magnetic induction equations using standard discontinuous Lagrange basis functions. The semi-discrete scheme is constructed by using the symmetrized version of the equation as introduced by Godunov. The resulting schemes are shown to be stable. Numerical experiments are performed in order to demonstrate the accuracy and convergence of the DG scheme through the L2-error and divergence error analysis. In the presence of discontinuities we add an artificial viscosity term to stabilize the solution. © 2018 IMACS