Nodal-based finite element methods with local projection stabilization for linearized incompressible magnetohydrodynamics

We consider the linearized resistive magnetohydrodynamics (MHD) model in incompressible media and its numerical solution. Conforming nodal-based finite element approximations of the MHD model both for inf-sup stable and equal order finite elements with respect to velocity and pressure are considered. As opposed to a residual-based stabilization method by Badia et al. (2013), we consider a local projection stabilization for the numerical solution. A detailed stability and error analysis for the arising discrete problem is given. Some numerical experiments like Hartmann’s MHD problem and singular solutions are examined.