A priori error analysis of a discontinuous Galerkin scheme for the magnetic induction equation

Abstract

We perform the error analysis of a stabilized discontinuous Galerkin scheme for the initial boundary value problem associated with the magnetic induction equations using standard discontinuous Lagrange basis functions. In order to obtain the quasi-optimal convergence incorporating second-order Runge-Kutta schemes for time discretization, we need a strengthened 4/3-CFL condition (∆t ∼ h4/3). To overcome this unusual restriction on the CFL condition, we consider the explicit third-order Runge-Kutta scheme for time discretization. We demonstrate the error estimates in L2-sense and obtain quasi-optimal convergence for smooth solution in space and time for piecewise polynomials with any degree l ≥ 1 under the standard CFL condition. © 2020 De Gruyter. All rights reserved.