Finite Element Iterative Methods for the 3D Steady Navier–Stokes Equations |
| |
Authors: | Yinnian He |
| |
Institution: | School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China; |
| |
Abstract: | In this work, a finite element (FE) method is discussed for the 3D steady Navier–Stokes equations by using the finite element pair . The method consists of transmitting the finite element solution of the 3D steady Navier–Stokes equations into the finite element solution pairs based on the finite element space pair of the 3D steady linearized Navier–Stokes equations by using the Stokes, Newton and Oseen iterative methods, where the finite element space pair satisfies the discrete inf-sup condition in a 3D domain . Here, we present the weak formulations of the FE method for solving the 3D steady Stokes, Newton and Oseen iterative equations, provide the existence and uniqueness of the FE solution of the 3D steady Stokes, Newton and Oseen iterative equations, and deduce the convergence with respect to of the FE solution to the exact solution of the 3D steady Navier–Stokes equations in the norm. Finally, we also give the convergence order with respect to of the FE velocity to the exact velocity u of the 3D steady Navier–Stokes equations in the norm. |
| |
Keywords: | Navier– Stokes equations Oseen iterative equations Newton iterative equations Stokes iterative equations weak formulation finite element error estimate discrete inf-sup condition |
|
|