| Chinese abstract | 第1-9页 |
| English abstract | 第9-14页 |
| Chapter 1. Domain Decomposition Method for Parabolic Equation with Discontinuous Coefficients and Parabolic Equations Systems | 第14-48页 |
| ·Introduction | 第14-15页 |
| ·Domain Decomposition Method for Parabolic Equation with Discontinuous Coefficients | 第15-26页 |
| ·Preliminary | 第16-17页 |
| ·Numerical Method | 第17-18页 |
| ·Numerical Analysis | 第18-25页 |
| ·Domain Decomposition Procedure with Moving Grid Method | 第25页 |
| ·Numerical Experiments | 第25-26页 |
| ·Domain Decomposition Procedure Modified by Characteristic Finite Element Method for System of Parabolic Equations with Discontinuous Coefficients13 | 第26-39页 |
| ·Numerical Method | 第27-30页 |
| ·Numerical Analysis | 第30-39页 |
| ·Domain Decomposition Method Modified with Characteristic Finite Element Procedure for A Type of Parabolic System | 第39-48页 |
| ·Numerical Method | 第39-41页 |
| ·Numerical Analysis | 第41-48页 |
| Chapter 2. Domain Decomposition Method for Integro-Differential Equation | 第48-69页 |
| ·Introduction | 第48-49页 |
| ·Domain Decomposition Moving Grid Finite Element Method for Integro-Differential Equation | 第49-56页 |
| ·Numerical Method | 第49-51页 |
| ·Convergence Analysis | 第51-56页 |
| ·Explicit/Implicit Domain Decomposition Procedure for Nonlinear Integro-Differential Equation | 第56-69页 |
| ·Numerical Method | 第57-59页 |
| ·Numerical Analysis | 第59-67页 |
| ·Numerical Experiments | 第67-69页 |
| Chapter 3. Domain Decomposition Method Modified with Characteristic Finite Element Procedure for Miscible Displacement in Porous Media | 第69-86页 |
| ·Introduction | 第69-71页 |
| ·Domain Decomposition Procedure Modified with Characteristic Finite Element Method for Miscible Displacement in Porous Media | 第71-81页 |
| ·Numerical Method | 第71-73页 |
| ·Numerical Analysis | 第73-80页 |
| ·Numerical Experiments | 第80-81页 |
| ·Domain Decomposition Procedure Modified with Characteristic Mixed Finite Element Method for Miscible Displacement in Porous Media | 第81-86页 |
| ·Numerical Algorithm | 第81-83页 |
| ·Convergence Analysis | 第83-84页 |
| ·Numerical Experiments | 第84-86页 |
| Chapter 4. An Optimization-Based Domain Decomposition for A Type of Parabolic Equations | 第86-98页 |
| ·Introduction | 第86-88页 |
| ·The Existence of An Optimal Solution | 第88-90页 |
| ·Convergence with Vanishing Penalty Parameter | 第90-91页 |
| ·The Optimality System | 第91-93页 |
| ·Finite Element Approximations | 第93-98页 |
| Reference | 第98-102页 |
| Acknowledgements | 第102-103页 |
| Curriculum Vitae | 第103-104页 |
