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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 strengthened4/3{4/3}-CFL condition (Δ⁢t∼h4/3{\Delta t\sim h^{4/3}}). 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 inL2{L^{2}}-sense and obtain quasi-optimal convergence for smooth solution in space and time for piecewise polynomials with any degreel≥1{l\geq 1}under the standard CFL condition.

A Priori Error Analysis of a Discontinuous Galerkin Scheme for the Magnetic Induction Equation