| 摘要 | 第8-9页 |
| Abstract | 第9-10页 |
| Introduction | 第11-16页 |
| Chapter 1 The characteristic variational multiscale method for convection-dominated convection-diffusion-reaction problems | 第16-37页 |
| 1.1 The characteristic variational multiscale method | 第16-21页 |
| 1.2 Stability analysis for the C-VMS method | 第21-23页 |
| 1.3 The convergence of the C-VMS method | 第23-26页 |
| 1.4 Numerical experiments | 第26-37页 |
| 1.4.1 Example 1-Convergence rate and CPU time | 第26-32页 |
| 1.4.2 Example 2-A rotating Gaussian benchmark | 第32-34页 |
| 1.4.3 Example 3-L-shaped domain | 第34-35页 |
| 1.4.4 Example 4-Three-dimensional case | 第35-37页 |
| Chapter 2 Analysis of the nonstationary Navier-Stokes problem by a novel characteristic stabilized finite element method | 第37-58页 |
| 2.1 Notations and Preliminaries | 第37-38页 |
| 2.2 The novel characteristic stabilized finite element method | 第38-41页 |
| 2.3 Stability analysis and error estimates | 第41-49页 |
| 2.4 Numerical experiments | 第49-58页 |
| 2.4.1 Example 1-A numerical example with the exact solution | 第49-52页 |
| 2.4.2 Example 2-Channel flow around a cylinder | 第52-55页 |
| 2.4.3 Example 3-The lid driven cavity problem | 第55-58页 |
| Chapter 3 Implicit-explicit time stepping scheme based on the streamline diffusion method for fluid-fluid interaction problems | 第58-79页 |
| 3.1 Notations and Preliminaries | 第58-60页 |
| 3.2 Implicit-explicit time stepping scheme based on the streamline diffusion method | 第60-62页 |
| 3.3 Stability analysis and error estimates | 第62-73页 |
| 3.4 Numerical experiments | 第73-79页 |
| 3.4.1 Example 1-Convergence rate and CPU time | 第73-76页 |
| 3.4.2 Example 2-Convex domain | 第76-78页 |
| 3.4.3 Example 3-Nonconvex domain | 第78-79页 |
| Chapter 4 Local projection stabilized and characteristic decoupled scheme for the fluid-fluid interaction problems | 第79-101页 |
| 4.1 Notations and Preliminaries | 第79-82页 |
| 4.2 LPSCD scheme | 第82-86页 |
| 4.3 Stability analysis | 第86-90页 |
| 4.4 Numerical experiments | 第90-101页 |
| 4.4.1 Example 1-Convergence rate and CPU time | 第90-95页 |
| 4.4.2 Example 2-Kinetic energy at the interface | 第95-97页 |
| 4.4.3 Example 3-Complex 2D domain | 第97-101页 |
| Chapter 5 Conclusions and Future Work | 第101-102页 |
| Bibliography | 第102-109页 |
| Publications and Finished Papers | 第109-110页 |
| Acknowledgements | 第110页 |
