A numerical study of a first order modular grad-div stabilization for the magnetohydrodynamics equations

This paper proposes a stabilization method to approximate analytical solutions of magnetohydrodynamics (MHD) equations. The method adds two modular grad-div steps into fully-discrete finite element MHD solver. The main idea in these intrusive steps is to penalize the divergence of the velocity/magnetic fields both in L2 and H1-norms. The paper confirms the optimal convergence of the method, and gives numerical experiments which reveal positive effect of the method as in the usual grad-div stabilization.