Quasi-least square finite element methods for stationary incompressible
magnetohydrodynamics problems
Abstract
This article aims to study the Quasi-least square mixed finite element
(FE) method for the approximate solution of Magnato-Hydro-Dynamic
equations (MHD). The resulting non-linear system of equations are
linearized around a characteristic state, resulting in first order
linearized least-square models that yield algebraic system of equations
with symmetric positive definite coefficient matrices. A central feature
of the method is that it does not require (Ladyzhenskaya-Babuska-Brezzi)
LBB conditions on the finite dimensional subspaces and the resulting
bilinear form is symmetric and positive definite. Secondly, it only
needs to choose the value of a single parameter to find the
well-posedness of the model equations. For the theoretical accuracy and
authentication of the method, we investigate existence of the solutions
and obtain a priori error estimates. The variables are fluid velocity,
fluid pressure and magnetic field. Numerical tests are performed in
order to assess the stability and the accuracy of the resulting methods.
Result shows good agreement with analytical solutions.