| 摘要 | 第1-9页 |
| Abstract | 第9-11页 |
| Introduction | 第11-15页 |
| Chapter 1 Preliminaries | 第15-19页 |
| ·The space H(div;D) | 第16-17页 |
| ·The space H(curl;D) | 第17-19页 |
| ·The space H(curl;D)in R~2 | 第17-18页 |
| ·The space H(curl;D)in R~3 | 第18-19页 |
| Chapter 2 A Priori and a Posteriori Error Estimates for H(div)-Elliptic Problem with Interior Penalty Method | 第19-52页 |
| ·Discontinuous Galerkin formulation for H(div)-elliptic problem | 第19-22页 |
| ·A priori error analysis | 第22-26页 |
| ·A posteriori error analysis | 第26-46页 |
| ·Reliability | 第32-40页 |
| ·Efficiency | 第40-46页 |
| ·Numerical experiments | 第46-52页 |
| Chapter 3 A Parallel Robin-Robin Domain Decomposition Method for H(div)-Elliptic Problem | 第52-70页 |
| ·State of the problem and preliminaries | 第52-55页 |
| ·The transmission condition on subdomain interfaces | 第55-57页 |
| ·The convergence of the domain decomposition method for the continuous problem | 第57-60页 |
| ·The convergence of the domain decomposition method for the discrete problem | 第60-67页 |
| ·Numerical experiments | 第67-70页 |
| Chapter 4 Optimization-Based Domain Decomposition Methods for H(div)-Elliptic Problem | 第70-81页 |
| ·Domain decomposition method for H(div)-ellliptic problem | 第70-78页 |
| ·Algorithm 1 | 第74-76页 |
| ·Algorithm 2 | 第76页 |
| ·Algorithm 3 | 第76-78页 |
| ·Numerical experiments | 第78-81页 |
| Chapter 5 Unified Framework for an a posteriori Error Analysis of Non-Standard Finite Element Approximations of H(div)-Elliptic Problem | 第81-89页 |
| ·The unified framework | 第81-85页 |
| ·Application to interior penalty discontinuous Galerkin method | 第85-89页 |
| Chapter 6 An Unfitted Penalty Finite Element Method for H(div)-Elliptic Interface Problem | 第89-99页 |
| ·Formulation of the penalty finite element method (PFEM) | 第89-92页 |
| ·Error estimates for the penalty finite element method | 第92-99页 |
| Chapter 7 Conclusions and Future Work | 第99-100页 |
| Bibliography | 第100-108页 |
| Publications and Finished Papers | 第108-109页 |
| Acknowledgements | 第109页 |
