该书结合作者的科研成果,介绍了偏微分方程有限元方法中的若干经典及前沿专题。

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Selected Topics in Finite Element Methods : [英文] = 有限元方法选讲

Selected Topics in Finite Element Methods (In English)

Microsoft Word - stif FM_new_.doc

Administrator

陈志明,武海军

中国美术学院出版社

科学出版社

1, Series in information and computational science, 2010-08

Xin xi yu ji suan ke xue cong shu, Di 1 ban, Beijing, 2010

China, People's Republic, China

1991

producers:
Acrobat Distiller 7.0 (Windows)

目录 8
Preface 6
Chapter 1 Variational Formulation of Elliptic Problems 11
1.1 Basic concepts of Sobolev space 11
1.2 Variational formulation 18
1.3 Exercises 21
Chapter 2 Finite Element Methods for Elliptic Equations 23
2.1 Galerkin method for variational problems 23
2.2 The construction of finite element spaces 25
2.2.1 The finite element 25
2.3 Computational consideration 30
2.4 Exercises 34
Chapter 3 Convergence Theory of Finite Element Methods 35
3.1 Interpolation theory in Sobolev spaces 35
3.2 The energy error estimate 41
3.3 The L 2 error estimate 42
3.4 Exercises 43
Chapter 4 Adaptive Finite Element Methods 44
4.1 An example with singularity 44
4.2 A posteriori error analysis 46
4.2.1 The Clement interpolation operator 46
4.2.2 A posteriori error estimates 49
4.3 Adaptive algorithm 51
4.4 Convergence analysis 52
4.5 Exercises 56
Chapter 5 Finite Element Multigrid Methods 57
5.1 The model problem 57
5.2 Iterative methods 58
5.3 The multigrid V-cycle algorithm 61
5.4 The finite element multigrid V-cycle algorithm 67
5.5 The full multigrid and work estimate 68
5.6 The adaptive multigrid method 69
5.7 Exercises 70
Chapter 6 Mixed Finite Element Methods 71
6.1 Abstract framework 71
6.2 The Poisson equation as a mixed problem 76
6.3 The Stokes problem 80
6.4 Exercises 83
Chapter 7 Finite Element Methods for Parabolic Problems 84
7.1 The weak solutions of parabolic equations 84
7.2 The semidiscrete approximation 88
7.3 The fully discrete approximation 92
7.4 A posteriori error analysis 96
7.5 The adaptive algorithm 102
7.6 Exercises 107
Chapter 8 Finite Element Methods for Maxwell Equations 108
8.1 The function space H(curl;Ω) 109
8.2 The curl conforming finite element approximation 116
8.3 Finite element methods for time harmonic Maxwell equations 121
8.4 A posteriori error analysis 124
8.5 Exercises 130
Chapter 9 Multiscale Finite Element Methods for Elliptic Equations 132
9.1 The homogenization result 132
9.2 The multiscale finite element method 136
9.2.1 Error estimate when h ε 138
9.3 The over-sampling multiscale finite element method 141
9.4 Exercises 147
Chapter 10 Implementations 148
10.1 A brief introduction to the MATLAB PDE Toolbox 148
10.1.1 A first example—Poisson equation on the unit disk 149
10.1.2 The mesh data structure 150
10.1.3 A quick reference 153
10.2 Codes for Example 4.1—L-shaped domain problem on uniform meshes 154
10.2.1 The main script 154
10.2.2 H1 error 155
10.2.3 Seven-point Gauss quadrature rule 155
10.3 Codes for Example 4.6|L-shaped domain problem on adaptive meshes 156
10.4 Implementation of the multigrid V-cycle algorithm 158
10.4.1 Matrix versions for the multigrid V-cycle algorithm and FMG 158
10.4.2 Code for FMG 159
10.4.3 Code for the multigrid V-cycle algorithm 160
10.4.4 The"newest vertex bisection"algorithm for mesh refinements 162
10.5 Exercises 168
Bibliography 170
参考文献 8

2025-10-27