Solution of Steady Incompressible MHD Problems with Quasi-Least Square Method

A quasi-least-squares (QLS) mixed finite element method (MFE) based on the L2-inner product is utilized to solve an incompressible magnetohydrodynamic (MHD) model. These models are associated with three unknown terms, i.e., fluid velocity, pressure, and magnetic field. For MHD-based models, common theories algorithms for approximation of solutions not always applicable because choice functional spaces during utilization weak formulation. It well known that used different unknowns, e.g., cannot be chosen independently variational formulation, may have satisfy strict stability conditions such as inf-sup, or Ladyzhenskaya–Babuska–Brezzi (LBB) condition. The dependency selection unknowns critical some pair unknowns. Because this, numerical theoretical must face issue. proposed scheme (L2-inner product) introduced circumvent this deficiency (inf-sup LBB) obtained a well-posed solution theoretically. model equations nonlinear highly coupled combination Navier–Stokes Maxwell relations. First, these made linear around specific state wherein modified system represents algebraic equation in first-order symmetric form. Secondly, direct iteration technique applied nonlinearities obtain convergent rate general initial guess. Theoretical results show only single parameter guess sufficient establish well-posedness solution.