An arbitrary high-order Spectral Difference method for the induction equation

We study in this paper three variants of the high-order Discontinuous Galerkin (DG) method with Runge-Kutta (RK) time integration for induction equation, analysing their ability to preserve divergence-free constraint magnetic field. To quantify divergence errors, we use a norm based on both surface term, measuring global and volume local errors. This leads us design new, arbitrary numerical scheme equation multiple space dimensions, modification Spectral Difference (SD) [1] ADER [2]. It appears as natural extension Constrained Transport (CT) method. show that it preserves ∇⋅B→=0 exactly by construction, sense. compare our new 3 RKDG energy evolution solution maps SD-ADER are qualitatively similar variant cleaning, but without need an additional extra variable control