Piecewise Bilinear Approximations to the 2-D Stationary Incompressible Navier-Stokes Problem by Least-Squares Finite Element Methods
| Autor: | Chun-Ting Li, 李俊廷 |
|---|---|
| Rok vydání: | 2004 |
| Druh dokumentu: | 學位論文 ; thesis |
| Popis: | 92 In this thesis, we study the piecewise bilinear finite element approximations to the two-dimensional stationary incompressible Navier-Stokes equations with the velocity boundary condition by using the least-squares principles. The Navier-Stokes problem is first recast into the velocity-vorticity-pressure and velocity-vorticity-total pressure first-order systems by introducing the vorticity variable and, in addition, total pressure variable. We then apply both the L2 least-squares and mesh-dependent weighted least-squares finite element schemes to approximate the solutions of the sequence of Oseen problems arising from a Picard-type iteration associated with these first-order systems. The corresponding least-squares energy functionals are defined in terms of the sum of the squared L2 norms without or with mesh-dependent weights of the residual equations over a product function space. Numerical evidences show that, for low Reynolds number flows, the L2 least-squares method is more accurate than the mesh-dependent weighted least-squares method. For flows with large Reynolds numbers, the mesh-dependent weighted least-squares method is apparently better than the L2 least-squares method. Some numerical results for driven cavity flows with various Reynolds numbers are also given. |
| Databáze: | Networked Digital Library of Theses & Dissertations |
| Externí odkaz: |
|