标题：椭圆方程有限元方法的整体超收敛及其应用
基本信息
出版社: 科学出版社有限责任公司; 第1版 (2012年3月1日) 
外文书名:Global Superconvergence of Finite Elements for Elliptic Equatio  椭圆方程有限元方法的整体超收敛及其应用ns and Ints Appli
精装: 324页 
正文语种: 英语 
开本: 16 
ISBN: 9787030334794 
条形码: 9787030334794 
商品尺寸: 24.2 x 17.2 x 2.2 cm 
商品重量: 658 g 
内容简介
《椭圆方程有限元方法的整体超收敛及其应用(英文版)》总结了作者及合作者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。 
编辑推荐
《椭圆方程有限元方法的整体超收敛及其应用(英文版)》由科学出版社有限责任公司出版。 
目录
Preface
Acknowledgements
Chapter I Basic Approaches
1.1 Introduction
1.2 Simplified Hybrid Combined Methods
1.3 Basic Theorem for Global Superconvergenee
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
3.4.2 Special case of h = k and
3.4.3 Comparisons
3.4.4 Relation between Uh and
3.5 Concluding Remarks
Chapter 4 Simplified Hybrid Method for Motz's Problems
4.1 Introduction
4.2 Simplified Hybrid Combined Methods
4.3 Lagrange Rectangular Elements
4.4 Adini's Elements
4.5 Concluding Remarks
Chapter 5 Finite Difference Methods for Singularity Problem
5.1 Introduction
5.2 The Shortley-Weller Difference Approximation
5.3 Analysis for uD with no Error of Divergence Integration
5.4 Analysis for Uh with Approximation of Divergence Integration..
5.5 Numerical Verification on Reduced Convergence Rates
5.5.1 The model on stripe domains
5.5.2 The Richardson extrapolation and the least squares method 
5.6 Concluding Remarks
Chapter 6 Basic Error Estimates for Biharmonic Equations ..
Chapter 7 Stability Analysis and Superconvergence of Blending
Problems
7.1 Introduction
7.2 Description of Numerical Methods
7.3 Stability Analysis
7.3.1 Optimal convergence rates and the uniform V-elliptic inequality.
7.3.2 Bounds of condition number
7.3.3 Proof for Theorem 7.3.4
7.4 Global Superconvergence
7.5 Numerical Experiments and Other Kinds of Superconvergence.. -
7.5.1 Verification of the analysis in Section 7.3 and Section 7.4
7.5.2 New superconvergence of average nodal solutions
7.5.3 Superconvergence of L-norm
7.5.4 Global superconvergence of the a posteriori interpolant solutions
7.6 Concluding Remarks
Chapter 8 Blending Problems in 3D with Periodical Boundary
Conditions
8.1 Introduction
8.2 Biharmouic Equations
8.2.1 Description of numerical methods
8.2.2 Global superconvergence
8.3 The BPH-FEM for Blending Surfaces
8.4 Optimal Convergence and Numerical Stability
8.5 Superconvergence
Chapter 9 Lower Bounds of Leading Eigenvalues
9.1 Introduction
9.1.1 Bilinear element Q1
9.1.2 Rotated Q1 element (Qot)
9.1.3 Extension of rotated Qz element (EQrzt)
9.1.4 Wilson's element
9.2 Basic Theorems
9.3 Bilinea Elements
9.4 QOt and EQrlt Elements
9.4.1 Proof of Lemma 9.4.1
9.4.2 Proof of Lemma 9.4.2
9.4.3 Proof of Lemma 9.4.3
9.4.4 Proof of Lemma 9.4.4
9.5 Wilson's Element
9.5.1 Proof of Lemma 9.5.1
9.5.2 Proof of Lemma 9.5.2
9.5.3 Proof of Lemma 9.5.3 and Lemma 9.5.4
9.6 Expansions for Eigenfunctiens
9.7 Numerical Experiments
9.7.1 Function p=1
9.7.2 Function p=0
9.7.3 Numerical conclusions
Chapter 10 Eigenvalue Problems with Periodical Boundary Conditions
10.1 Introduction
10.2 Periodic Boundary Conditions
10.3 Adini's Elements for Eigenvalue Problems
10.4 Error Analysis for Poisson's Equation
10.5 Superconvergence for Eigenvalue Problems
10.6 Applications to Other Kinds of FEMs
10.6.1 Bi-quadratic Lagrange elements
10.6.2 Triangular elements
10.7 Numerical Results
10.8 Concluding Remarks
Chapter 11 Semilinear Problems
11.1 Introduction
11.2 Parameter-Dependent Semilinear Problems
11.3 Basic Theorems for Superconvergence of FEMs
11.4 Superconvergence of Bi-p(> 2)-Lagrange Elements
11.5 A Continuation Algorithm Using Adini's Elements
11.6 Conclusions
Chapter 12 Epilogue
12.1 Basic Framework of Global Superconvergence
12.2 Some Results on Integral Identity Analysis
12.3 Some Results on Global Superconvergence
Bibliography
Index