| Abstract (In English) | 第1-10页 |
| Abstract (In Chinese) | 第10-14页 |
| Chapter 1 Analysis of The Finite Element Approximation for Two-phase Miscible Displacement in Porous Media | 第14-59页 |
| ·Introduction | 第14-17页 |
| ·Finite Volume Method for Two-Phase Incompressible Flow in Porous Media | 第17-36页 |
| ·Notation, assumptions and preliminaries | 第17-18页 |
| ·The finite volume element | 第18-21页 |
| ·Auxiliary lemmas | 第21-22页 |
| ·Error estimate in H~1 | 第22-29页 |
| ·Error estimate in L~2 | 第29-34页 |
| ·Numerical example | 第34-36页 |
| ·An Upwinding-Mixed Method for Positive Semi-definite Miscible Displacement Problem in Multidimension | 第36-50页 |
| ·Notation, assumptions and preliminaries | 第36-38页 |
| ·The upwind-mixed scheme | 第38-39页 |
| ·The principle of mass conservation and the auxiliary lemmas | 第39-42页 |
| ·Error estimate | 第42-45页 |
| ·The upwind-mixed method for positive definite problem | 第45-47页 |
| ·Numerical experiment | 第47-50页 |
| ·An Upwinding-Mixed Multistep Method for Positive Semi-definite Miscible Displacement Problem | 第50-59页 |
| ·Preliminaries and notation | 第50页 |
| ·The upwind-mixed multistep scheme | 第50-52页 |
| ·Error estimate | 第52-56页 |
| ·Numerical example | 第56-59页 |
| Chapter 2 Analysis of A Godunov-Mixed Finite Element Method for Con?taminant Transport Equations in Two Dimensions | 第59-78页 |
| ·Introduction | 第59-61页 |
| ·Analysis of A Godunov-Mixed Finite Element Method for Contaminant Trans?port Equations in Two Dimensions: Equilibrium Adsorption Processes | 第61-69页 |
| ·Assumptions and preliminaries | 第62页 |
| ·The semi-discrete Godunov-mixed scheme | 第62-64页 |
| ·Auxiliary lemmas | 第64-66页 |
| ·Analysis of the semi-discrete scheme | 第66-69页 |
| ·Analysis of A Godunov-Mixed Finite Element Method for Contaminant Trans?port Equations in Two Dimensions: Nonequilibrium Adsorption Processes | 第69-78页 |
| ·Assumptions and Preliminaries | 第70页 |
| ·A fully discrete Godunov-mixed scheme | 第70-71页 |
| ·Convergence analysis | 第71-77页 |
| ·Numerical experiment | 第77-78页 |
| Chapter 3 The Finite Element Methods on Dynamically Changing Meshes | 第78-106页 |
| ·Introduction | 第78-79页 |
| ·The Alternating-Direction Method with Moving Mesh for Nonlinear Parabolic Problem | 第79-86页 |
| ·The alternating-direction with moving mesh | 第80-81页 |
| ·Convergence analysis | 第81-85页 |
| ·Numerical example | 第85-86页 |
| ·The Alternating-Direction Galerkin Method with Moving Mesh for Nonlinear Hyperbolic Problem | 第86-96页 |
| ·The model and notation, assumptions and preliminaries | 第86-87页 |
| ·The alternating-direction Galerkin method with moving mesh | 第87-89页 |
| ·Convergence analysis | 第89-95页 |
| ·Numerical example | 第95-96页 |
| ·Upwind-Mixed Method on A Dynamically Changing Mesh for Positive Semidefinite Problem of Two Phase Miscible Flow in Porous Media | 第96-106页 |
| ·The preliminaries and notation | 第97-98页 |
| ·The scheme of the positive semi-definite problem | 第98-100页 |
| ·The scheme of the positive definite problem | 第100-102页 |
| ·The modified scheme | 第102-104页 |
| ·Numerical example | 第104-106页 |
| Bibliography | 第106-111页 |
| Acknowledgment | 第111-112页 |
| List of publications | 第112-113页 |
| The brief introduction of the author (in Chinese) | 第113-114页 |
