Magnetohydrodynamics (MHD) simulation via an adaptive element free Galerkin method

In this work, an adaptive element free Galerkin technique is presented to solve magnetohydrodynamics (MHD) equations. An a posteriori error estimation based on gradient recovery is suggested to find locations with largest error contribution. For stabilization, the MHD equations are converted into two convection diffusion equations and these equations are stabilized by adding an artificial diffusion based on local Peclet number. The presented numerical examples show efficiency of the adaptive technique.