Defect correction finite element method for the stationary incompressible Magnetohydrodynamics equation

Abstract

In this study, we give the defect correction finite element method for the stationary incompressible MHD equation. Firstly, the nonlinear MHD equation is solved with an artificial viscosity term. Then, the numerical solution is improved on the same grid by a linearized defect-correction technique. Then, we give the numerical analysis including stability analysis and error analysis. The numerical analysis proves that our method is stable and has an optimal convergence rate. Then, we give some numerical results. From the numerical results, we can see that our method is efficient for solving the MHD equations.