Projection Scheme And Penalty Approximation For A Coupled System Arising In Magnetohynamic Problem

In this thesis,we focus on a magnetohydrodynamics equations cou-pled by nonstationary navier-stokes equations and stationary Maxwell equations.The main contents of this thesis include:1.Based on the discrete time first-order backward Euler scheme,structure to solve a class of incompressible MHD equations with weak coupling form of projection methods,the algorithm is energy and at the discrete level accurately meet no divergence condition of velocity field.Under the assumption of the regularity of the solution,we prove that the scheme has the optimal first-order time convergence accuracy when the time step is small enough.The corresponding numerical results verify the effectiveness of the scheme and theory analysis;2.By introducing the penalty parameter ?,the penalty approx-imation system is proposed,and the error estimate between the true solution and the approximate solution is established.