A conservative stabilized finite element method for the magneto-hydrodynamic equations

This work presents a finite element solution of the 3D magneto-hydrodynamics equations. The formulation takes explicitly into account the local conservation of the magnetic field, giving rise to a conservative formulation and introducing a new scalar variable. A stabilization technique is used in order to allow equal linear interpolation on tetrahedral elements of all the variables. Numerical tests are performed in order to assess the stability and the accuracy of the resulting methods. The convergence rates are calculated for different stabilization parameters. Well-known MHD benchmark tests are calculated. Results show good agreement with analytical solutions.