| 摘要 | 第6-8页 |
| Abstract | 第8-9页 |
| Chapter 1 Introduction | 第10-16页 |
| 1.1 The immersed method | 第10-14页 |
| 1.2 The high-order compact FVE method | 第14-16页 |
| Chapter 2 The immersed finite volume element method for the elliptic in-terface problem | 第16-52页 |
| 2.1 The quadrilateral grids for the constant coefficients case | 第16-29页 |
| 2.1.1 The problem and a brief review of the source removal technique | 第16-19页 |
| 2.1.2 The immersed finite volume element method | 第19-25页 |
| 2.1.3 Numerical experiments | 第25-29页 |
| 2.2 The triangular grids for the discontinuous variable coefficients case | 第29-52页 |
| 2.2.1 The problem and a brief review of the source removal technique | 第29-31页 |
| 2.2.2 The immersed finite volume element formulation | 第31-33页 |
| 2.2.3 The construction of basis functions | 第33-35页 |
| 2.2.4 The reasons for choosing triangular grids | 第35-36页 |
| 2.2.5 The numerical schemes | 第36-39页 |
| 2.2.6 The error estimate of the immersed finite volume element method | 第39-46页 |
| 2.2.7 Numerical experiments | 第46-52页 |
| Chapter 3 A high-order compact finite volume element method for the dual-phase lag(DPL)heat conduction equations with an interface | 第52-95页 |
| 3.1 The description of the problem | 第52-54页 |
| 3.2 The numerical schemes | 第54-64页 |
| 3.3 Error analysis and estimate | 第64-86页 |
| 3.4 Numerical experiments | 第86-89页 |
| 3.5 The Pade compact finite volume method | 第89-94页 |
| 3.6 Conclusions | 第94-95页 |
| Chapter 4 Conclusions and Future work | 第95-97页 |
| Bibliography | 第97-101页 |
| Publications and Finished Papers | 第101-102页 |
| Acknowledgements | 第102页 |
