Numerical Analysis and Comparison of Three Iterative Methods Based on Finite Element for the 2D/3D Stationary Micropolar Fluid Equations

Abstract

In this paper, three iterative methods (Stokes, Newton and Oseen iterative methods) based on finite element discretization for the stationary micropolar fluid equations are proposed, analyzed and compared. The stability and error estimation for the Stokes and Newton iterative methods are obtained under the strong uniqueness conditions. In addition, the stability and error estimation for the Oseen iterative method are derived under the uniqueness condition of the weak solution. Finally, numerical examples test the applicability and the effectiveness of the three iterative methods.

Pressure stabilization method for the 2D/3D time‐dependent natural convection equations with salt concentration

“…NCSC can be studied with the help of successful experience in such equations. For dealing with nonlinear iteration problems, generally speaking, some of the most common iterations for fluid equations are adopted, that is Stokes iteration, Oseen iteration and Newton iteration [18,19], as well as fixed-point iteration [20], extrapolation iteration [21] and C-N scheme [22], and so forth.…”

Local discontinuous Galerkin method coupled with the implicit‐explicit Runge–Kutta method for the time‐dependent micropolar fluid equations

“…Chen et al 15 studied the projection method and space finite difference method to solve unsteady micropolar fluid equations. Xing et al 16 proposed numerical analysis and comparison of three iterative methods based on finite element for the 2D/3D stationary micropolar fluid equations.…”

Research on three kinds of splitting finite element schemes for 2D/3D unsteady incompressible thermomicropolar fluid equations

“…The Newton scheme can simulates very well even strong convection scenarios, but it requires some precision for the initial value. The computational cost and stability of the Oseen scheme are between Stokes scheme and Newton scheme 31‐33 . In addition, there are skew‐symmetric convection term, Crank‐Nicolson extrapolate and other methods to solve the nonlinear property 31,34,35 …”

“…The computational cost and stability of the Oseen scheme are between Stokes scheme and Newton scheme. [31][32][33] In addition, there are skew-symmetric convection term, Crank-Nicolson extrapolate and other methods to solve the nonlinear property. 31,34,35 In this article, we will propose a new class of unconditionally stable schemes, called splitting Oseen schemes.…”