An interior penalty Galerkin method for the MHD equations in heterogeneous domains

Abstract

The Maxwell equations in the magnetohydrodynamic (MHD) limit in heterogeneous domains composed of conducting and non-conducting regions are solved by using Lagrange finite elements and by enforcing continuities across interfaces using an Interior Penalty technique à la Baker [Finite element methods for elliptic equations using non-conforming elements, Math. Comp. 31 (137) (1977) 45–59]. The method is shown to be stable and convergent and is validated by convergence tests. It is used to compute Ohmic decay in various compact conducting domains and to simulate the kinematic dynamo action in two different geometries.