Stability analysis and error estimates of an exactly divergence-free method for the magnetic induction equations (Q2820339)

The paper under review deals with the study of the first order divergence-free method in connection with Cartesian meshes for the magnetic induction equations. This study is in strong relationship with the stability and numerical analysis of solutions of the ideal magneto-hydrodynamic equations. The authors are mainly concerned with the numerical stability, which is established through both energy and Fourier methods. This study is performed when the meshes are uniform and when the velocity field in the equations is constant. The authors also establish \textit{a priori} error estimates in the \(L^2\) norm for sufficiently smooth solutions.