Decoupled,Semi-implicit Scheme For A Coupled System Arising In Magnetohydrodynamics Problem

In this thesis,we focus on a magnetohydrodynamics equations’semi-implicit fully discrete Galerkin finite element scheme.The mag-netohydrodynamics equations are coupling the nonstationary Navier-Stokes equation with the stationary Maxwell’s equation.Furthermore,the constructed fully discrete scheme is decoupled and linear and easy to implement numerically.This thesis is organized by three main parts as follow:1.First of all,the regularities of the solution of the magnetohydro-dynamics equations are proved.2.At the temporal discretization level,we use the first order back-wards Euler scheme,and the time discrete scheme to solve the magne-tohydrodynamics equations have been given.Also,we have proved the well-posedness of the time discrete scheme’ solution;3.About the magnetic field,the velocity field and the pressure,we use the conforming Galerkin finite element approximation,and the first order semi-implicit fully discrete finite element scheme to solve the magnetohydrodynamics equations.Also,we obtain the finite element error estimates.In addition,we have presented a numerical experiment to verify the results of theoretical analysis by use the appropriate time step and mesh size.