| Chinese Abstract | 第1-10页 |
| English Abstract | 第10-15页 |
| Chapter 1 Analysis of Incompressible Miscible Displacement in Porous Media by Characteristics Collocation Method | 第15-36页 |
| ·Introduction | 第15-17页 |
| ·Fully Discrete Characteristic Collocation Scheme | 第17-20页 |
| ·Notations and definition for collocation methods | 第17-18页 |
| ·Fully discrete collocation scheme | 第18-20页 |
| ·Existence of Solution of CCS | 第20-26页 |
| ·Some lemmas | 第21-24页 |
| ·Existence of solution of CCS | 第24-26页 |
| ·Convergence Analysis | 第26-34页 |
| ·Important conclusion | 第26-29页 |
| ·Error estimate | 第29-34页 |
| ·Extensions and remarks | 第34-36页 |
| Chapter 2 The Characteristics Collocation Method for Compressible Miscible Displacement in Porous Media | 第36-48页 |
| ·Introduction | 第36-37页 |
| ·Fully Discrete Characteristic Collocation Scheme | 第37-40页 |
| ·Convergence Analysis | 第40-46页 |
| ·Existence of the solution of CCS | 第40页 |
| ·Error estimate | 第40-46页 |
| ·Conclusion and remarks | 第46-48页 |
| Chapter 3 The Parallel Subspace Correction Collocation Method for the Parabolic Equations | 第48-60页 |
| ·Introduction | 第48-50页 |
| ·Preliminaries | 第50-52页 |
| ·PSC collocation methods for the Parabolic Equation | 第52-60页 |
| ·Collocation method for the parabolic problem | 第52-54页 |
| ·Constructions of algorithms | 第54-56页 |
| ·Convergence theory | 第56-60页 |
| Chapter 4 Some Orthogonal Collocation Methods for the Hyperbolic Equations | 第60-83页 |
| ·Introduction | 第60-62页 |
| ·The orthogonal collocation method for the hyperbolic equations | 第62-67页 |
| ·Basic lemmas | 第62-64页 |
| ·Orthogonal collocation scheme and error estimate | 第64-67页 |
| ·ADI collocation method for the hyperbolic equations | 第67-77页 |
| ·Preliminaries | 第67-69页 |
| ·ADI collocation schemes and convergence analysis | 第69-75页 |
| ·Implentation of the schemes | 第75-77页 |
| ·PSC collocation method for the hyperbolic equations | 第77-83页 |
| ·PSC collocation algorithm | 第77-79页 |
| ·Convergcnce analysis | 第79-83页 |
| Chapter 5 Numerical Results and Future Work | 第83-90页 |
| ·Numerical experiments | 第83-88页 |
| ·Conclusion and future work | 第88-90页 |
| Bibliography | 第90-96页 |
| Acknowledgment | 第96-97页 |
| List of publications | 第97-98页 |
| Curriculum Vitae | 第98-99页 |
| 学位论文评阅及答辩情况表 | 第99页 |
