Numerical solutions of 3D MHD equations

In this thesis, we analyzed the numerical solutions of the 3D MagnetoHydroDynamic (MHD) equations. Firstly, both the Finite Element Method (FEM) and the Boundary Element Method (BEM) formulations of the Laplace equations are given in detail. Numerical solutions are obtained for the both method and compared. Next, the stabilized finite element method formulation of the convection-diffusion equations is proposed and stable solutions are obtained for the convection dominated case. Later, the proposed stabilized formulation is applied to the numerical solutions of the 3D MHD equations defined on either spherical or cubic domain. Finally, the most general case of the problem which is the 3D MHD equations on spherical or cubic domain defined on the infinite conducting medium is considered. The solutions are obtained for the different problem parameters and the detailed discussions are provided.