A parallel finite element method for incompressible magnetohydrodynamics equations

Abstract

Based on the partition of unity method (PUM), a parallel finite element method (FEM) is designed for stationary incompressible magnetohydrodynamics (MHD) equations. The nonlinear problem is solved globally on a coarse grid, and then correction subproblems on corresponding subdomains with fine meshes are computed in parallel by Picard iteration. The subdomains are generated by a class of partition of unity, which gives a flexible and controllable way to decompose the domain. The optimal error estimate is proved. The validity of the proposed algorithm is testified by numerical examples.