《椭圆方程有限元方法的整体超收敛及其应用(英文版)》总结了作者Zi-Cai Li、Hung-Tsai Huang、Ningning Yan近十几年来在有限元高精度算法（主要是整体超收敛分析）方面的主要结果，其中包括许多已发表或尚未发表的成果。本书采用统一的分析方法，即中国学者独创的积分恒等式方法，对常见的椭圆型偏微分方程的各种有限元方法进行了深入、系统的分析，给出了相应的整体超收敛结果及高精度有限元算法。该书还讨论了非线性问题、特征值问题及差分方法等的整体超收敛，研究了相应的稳定性分析和奇异问题的特殊处理技术，介绍了大量实际应用问题的超收敛分析和数值计算结果，以验证整体超收敛分析的有效性。

Preface

Acknowledgements

Chapter 1 Basic Approaches

 1.1 Introduction

 1.2 Simplified Hybrid Combined Methods

 1.3 Basic Theorem for Global Superconvergence

 1.4 Bilinear Elements

 1.5 Numerical Experiments

 1.6 Concluding Remarks

Chapter 2 Adini's Elements

 2.1 Introduction

 2.2 Adini's Elements

 2.3 Global Superconvergence

2.3.1 New error estimates

2.3.2 A posteriori interpolant formulas

 2.4 Proof of Theorem 2.3.1

2.4.1 Preliminary lemmas

2.4.2 Main proof of Theorem 2.3.1

 2.5 Stability Analysis

 2.6 New Stability Analysis via Effective Condition Number

2.6.1 Computational formulas

2.6.2 Bounds of effective condition number

 2.7 Numerical Experiments and Concluding Remarks

Chapter 3 Biquadratic Lagrange Elements

 3.1 Introduction

 3.2 Biquadratic Lagrange Elements

 3.3 Global Superconvergence

3.3.1 New error estimates

3.3.2 Proof of Theorem 3.3.1

3.3.3 Proof of Theorem 3.3.2

3.3.4 Error bounds for Q8 elements

 3.4 Numerical Experiments and Discussions

3.4.1 Global superconvergence

……

Chapter 4 Simplified Hybrid Method for Motz's Problems

Chapter 5 Finite Difference Methods for Singularity Problems

Chapter 6 Basic Error Estimates for Biharmonic Equations

Chapter 7 Stability Analysis and Superconvergence of Blending Problems

Chapter 8 Blending Problems in 3D with Periodical Boundary Conditions

Chapter 9 Lower Bounds of Leading Eigenvalues

Chapter 10 Eigenvalue Problems with Periodical Boundary Conditions

Chapter 11 Semilinear Problems

Chapter 12 Epilogue

Bibliography

Index