Stabilized discontinuous Galerkin scheme for the magnetic induction equation (Q1728333)

The authors investigate a special form of the well-known magneto-hydrodynamics model leading to the magnetic induction equation. A discontinuous Galerkin scheme is developed based on standard discontinuous Lagrange basis functions and using the symmetrized version of the equation as introduced previously by Godunov. Stability, accuracy and convergence of the proposed scheme are shown and confirmed already with numerical experimentations. A stability problem is controlled by an extra term due to an artificial viscosity. Overall, the arguments treated are important They lead to high accurate, convergent and stable algorithms. The paper is interesting and significant for the scientific community, especially in numerical studies.