《橢圓方程有限元方法的整體超收斂及其套用（英文版）》是2012年3月科學出版社出版的圖書，作者是Ningning Yan等。
基本介紹
內容簡介,作者簡介,目錄,
內容簡介
This book covers the advanced study on the global superconvegence of elliptic equations in both theory and computation， where the main materials are adapted from ourjournal papers published. A deep and rather completed analysis of global supperconvergence is explored for bilinear， biquadratic， Adini's and bi-cubic Hermite elements， as well as for the finite difference method. Poisson's and the biharmonic equations are included， and eigenvalue and semi-linear problems are discussed. The singularity problems， blending problems， coupling techniques， a posteriori interpolant techniques， and some physical and engineering problems are studied. Numerical examples are provided for verification of the analysis， and other numerical experiments can be found from our publications. This book has also summarized some important results of Lin， his colleagues and others. This book is written for researchers and graduate students of mathematics and engineering to study and apply the global superconvergence for numerical PDE.
作者簡介
Zi-Cai Li graduated in 1963 from Tsinghua University， and received the Ph. D. degree in 1986 from the University of Toronto. Since 1993， he has been a Professor in Department of Applied .Mathematics，Sun Yat-sen University， Kaohsiung， Taiwan. His research areas are numerical analysis， scientific computing， image processing and pattern recognition.
Hung-Tsai Huang is a Professor at Department of Applied Mathematics， I-Shou University， Kaohsiung， Taiwan. He received the Ph.D. degree in 2003 from the Department of Applied Mathematics， Sun Yat-sen University， Kaohsiung， Taiwan. His research areas are numericalanalysis and scientific computing.
Ningning Yan earned her Ph.D. from the Institute of Computational Mathematics， Chinese Academy of Sciences in 1990. She is currently the professor of Academy of Mathematics and Systems Science， Chinese Academy of Sciences. Her research interests are numerical methods for partial differential equations and optimal control problems.
目錄
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
Hung-Tsai Huang is a Professor at Department of Applied Mathematics， I-Shou University， Kaohsiung， Taiwan. He received the Ph.D. degree in 2003 from the Department of Applied Mathematics， Sun Yat-sen University， Kaohsiung， Taiwan. His research areas are numericalanalysis and scientific computing.
Ningning Yan earned her Ph.D. from the Institute of Computational Mathematics， Chinese Academy of Sciences in 1990. She is currently the professor of Academy of Mathematics and Systems Science， Chinese Academy of Sciences. Her research interests are numerical methods for partial differential equations and optimal control problems.
目錄
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
