| Abstract | 第1-10页 |
| Abstract (In Chinese) | 第10-13页 |
| Chapter 1 High Accuracy Finite Volume Element Methods On Triangular Meshes | 第13-36页 |
| §1.1 Quadratic Finite Volume Element Methods for Nonlinear Parabolic Systems | 第13-21页 |
| §1.1.1 Meshes and notation | 第13-15页 |
| §1.1.2 Some auxiliary results | 第15-18页 |
| §1.1.3 FVE scheme and error estimates | 第18-21页 |
| §1.1.4 Numerical experiment | 第21页 |
| §1.2 A Multistep Finite Volume Element Scheme Along Characteristics for Nonlinear Convection Diffusion Problems | 第21-29页 |
| §1.2.1 Meshes and notation | 第22-23页 |
| §1.2.2 Multistep FVE scheme and error estimates | 第23-28页 |
| §1.2.3 Numerical experiment | 第28-29页 |
| §1.3 Cubic Finite Volume Element Methods for Elliptic Equations With Variable Coefficients | 第29-36页 |
| §1.3.1 Notation and method | 第29-31页 |
| §1.3.2 Some auxiliary results | 第31-33页 |
| §1.3.3 Error estimates | 第33-34页 |
| §1.3.4 Numerical experiment | 第34-36页 |
| Caapter 2 Symmetric Finite Volume Element Methods Based On Linear Tensor Product Elements for 2-D And 3-D Convection Diffusion Problems | 第36-66页 |
| §2.1 Symmetric Finite Volume Element Methods Along Characteristics for 3-D Convection Diffusion Problems | 第36-50页 |
| §2.1.1 Meshes and notation | 第37-39页 |
| §2.1.2 Some auxiliary results | 第39-44页 |
| §2.1.3 Symmetric FVE scheme and error estimates | 第44-48页 |
| §2.1.4 Numerical experiment | 第48-50页 |
| §2.2 Symmetric Multistep Finite Volume Element Methods Along Characteristics for 2-D Nonlinear Convection Diffusion Problems | 第50-66页 |
| §2.2.1 Meshes and notation | 第50-52页 |
| §2.2.2 Some auxiliary results | 第52-55页 |
| §2.2.3 Symmetric multistep FVE scheme and error estimates | 第55-64页 |
| §2.2.4 Numerical experiment | 第64-66页 |
| Chapter 3 A Symmetric Finite Volume Element Scheme With Second Order Accuracy for Nonlinear Convection Diffusion Problems | 第66-76页 |
| §3.1 Introduction | 第66-67页 |
| §3.2 Meshes and notation | 第67-70页 |
| §3.3 Some auxiliary results | 第70-72页 |
| §3.4 Symmetric high accuracy FVE scheme and error estimates | 第72-74页 |
| §3.5 Numerical experiment | 第74-76页 |
| Chapter 4 Multistep Finite Volume Methods for Positive Semidefinite Two-Phase Incompressible Flow In Porous Media | 第76-90页 |
| §4.1 Introduction | 第76-77页 |
| §4.2 Multistep Finite Volume Scheme | 第77-79页 |
| §4.3 Error Estimates | 第79-88页 |
| §4.4 Numerical Experiment | 第88-90页 |
| References | 第90-94页 |
| Acknowledgments (In Chinese) | 第94-95页 |
| Curriculum Vitae (In Chinese) | 第95-96页 |
| 学位论文评阅及答辩情况表 | 第96页 |
