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. (C) 2016 Elsevier B.V. All rights reserved.