Least-Squares Finite Element Method for Solving Stokes Flow under Point Source Magnetic Field

Abstract

The least-squares finite element method (LSFEM) is successfully employed for the discretization of the Stokes equations and the numerical computation of the behaviour of two-dimensional Stokes flow in a straight rectangular channel under the effect of a point-source magnetic field. LSFEM has several advantages in terms of theory and computing, where it can always create a symmetric, positive-definite algebraic system of equations. It also allows for using an equal order shape function for both velocity and pressure, and it is not required to satisfy the Ladyzhenskaya–Babuška–Brezzi (LBB) condition. Despite this, LSFEM has an issue where low-order nodal expansions tend to lock. Thus, the present study proposes the discretization of the problem domain using higher-order nodes elements with full numerical integration. Results concerning velocity contour and streamlines pattern are shown. On the basis of current findings, it can be concluded that the LSFEM can be used to solve Stokes flow problem under the point source magnetic field.