在本篇論文中，我們主要研究穩態不可壓縮磁流體(MHD)問題的兩種皮卡型迭代最小平方有限元素法數值解。首先引入兩個新未知變數旋度和電流密度，我們可推得在速度-旋度-壓力-磁場-電流密度(VVPMC)形式下的非線性一階不可壓縮MHD問題。接著我們引用兩種皮卡型迭代最小平方有限元素法以求取此一階不可壓縮VVPMC MHD問題之數值解。在每一次皮卡型迭代中，使用加權或未加權的L2最小平方有限元素法求解其相對應的一階歐辛型的問題。針對各種不同流體雷諾數的一階歐辛型問題和非線性一階VVPMC MHD問題，數值實驗結果證明了此類最小平方有限元素法的精確度。最後，我們列出MHD流體通過某個階梯形流場的數值結果。 In this thesis, we study two Picard-type iterative least-squares finite element schemes for approximating the solution to the stationary incompressible magneto -hydrodynamic (MHD) problem. Introducing the additional vorticity and current density variables, we have the non-linear first-order incompressible MHD problem in the velocity-vorticity-pressure-magnetic field-current density (VVPMC) formulation. Two Picard-type iterative least-squares finite element schemes are then applied for finding the numerical solution of the first-order incompressible VVPMC MHD problem. In each Picard iteration, the L2 least-squares finite element scheme with or without weights is employed to approximate the solution of the associated first-order Oseen-type problem. Numerical experiments with various hydrodynamic Reynolds numbers for the first-order Oseen-type problem and the non-linear first-order VVPMC MHD problem are reported to demonstrate the accuracy of the least-squares finite element approach. Finally, numerical results of an MHD flow over a step are also given.
