【现货速发】最优控制问题高效高精度算法
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天津津南
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作者陈艳萍，鲁祖亮
出版社科学出版社
ISBN9787030463951
出版时间2021-06
装帧精装
开本16开
定价128元
货号23832499
上书时间2024-11-24
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导语摘要
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目录
Contents
Chapter 1 Introduction 1
Chapter 2 Some preliminaries 5
2.1 Sobolev spaces 5
2.2 Finite element methods for elliptic equations 8
2.2.1 A priori error estimates 9
2.2.2 A posteriori error estimates 15
2.2.3 Superconvergence 17
2.3 Mixed finite element methods 19
2.3.1 Elliptic equations 19
2.3.2 Parabolic equations 25
2.3.3 Hyperbolic equations 26
2.4 Optimal control problems 31
2.4.1 Backgrounds and motivations 31
2.4.2 Some typical examples 32
2.4.3 Optimality conditions 34
Chapter 3 Finite element methods for optimal control problems 36
3.1 Elliptic optimal control problems 36
3.1.1 Distributed elliptic optimal control problems 36
3.1.2 Finite element discretization 37
3.1.3 A posteriori error estimates 38
3.2 Parabolic optimal control problems 44
3.2.1 Fully discrete finite element approximation 45
3.2.2 Intermediate error estimates 46
3.2.3 Superconvergence 50
3.3 Optimal control problems with oscillating coefficients 54
3.3.1 Finite element scheme 55
3.3.2 Multiscale finite element scheme 56
3.3.3 Homogenization theory and related estimates 57
3.3.4 Convergence analysis59
3.4 Recovery a posteriori error estimates 63
3.4.1 Fully discrete finite element scheme 65
3.4.2 Error estimates of intermediate variables 65
3.4.3 Superconvergence 68
3.4.4 A posteriori error estimates 72
3.5 Numerical examples 74
3.5.1 Parabolic optimal control problems 74
3.5.2 Recovery a posteriori error estimates 77
Chapter 4 A priori error estimates of mixed finite element methods 81
4.1 Elliptic optimal control problems 81
4.1.1 Mixed finite element scheme 82
4.1.2 A priori error estimates 84
4.2 Parabolic optimal control problems 92
4.2.1 Mixed finite element discretization 92
4.2.2 Mixed method projection95
4.2.3 Intermediate error estimates 98
4.2.4 A priori error estimates 101
4.3 Hyperbolic optimal control problems 106
4.3.1 Mixed finite element methods 107
4.3.2 A priori error estimates 109
4.4 Fourth order optimal control problems 116
4.4.1 Mixed finite element scheme116
4.4.2 L2-error estimates 119
4.4.3 L∞-error estimates 124
4.5 Nonlinear optimal control problems 128
4.5.1 Mixed finite element discretization 129
4.5.2 Error estimates 131
4.6 Numerical examples 132
4.6.1 Elliptic optimal control problems 132
4.6.2 Fourth order optimal control problems 134
Chapter 5 A posteriori error estimates of mixed finite element methods .136
5.1 Elliptic optimal control problems 136
5.1.1 Mixed finite element discretization 136
5.1.2 A posteriori error estimates for control variable138
5.1.3 A posteriori error estimates for state variables 141
5.2 Parabolic optimal control problems 145
5.2.1 Mixed finite element approximation 146
5.2.2 A posteriori error estimates 148
5.3 Hyperbolic optimal control problems 161
5.3.1 Intermediate error estimates 161
5.3.2 A posteriori error estimates for control variable164
5.3.3 A posteriori error estimates for state variables 166
5.4 Nonlinear optimal control problems 175
5.4.1 Mixed finite element discretization 175
5.4.2 Intermediate error estimates 176
5.4.3 A posteriori error estimates 181
Chapter 6 Superconvergence of mixed finite element methods 183
6.1 Elliptic optimal control problems 183
6.1.1 Recovery operator 183
6.1.2 Superconvergence property 184
6.2 Parabolic optimal control problems 185
6.2.1 Superconvergence for the intermediate errors 189
6.2.2 Superconvergence 193
6.3 Hyperbolic optimal control problems 197
6.3.1 Superconvergence property 198
6.3.2 Superconvergence for the control variable 200
6.4 Nonlinear optimal control problems 201
6.4.1 Superconvergence for the intermediate errors 201
6.4.2 Global superconvergence207
6.4.3 H.1-error estimates 209
6.5 Numerical examples 211
6.5.1 Elliptic optimal control problems 211
6.5.2 Nonlinear optimal control problems 213
Chapter 7 Finite volume element methods for optimal control problems 216
7.1 Elliptic optimal control problems 216
7.1.1 Finite volume element methods 218
7.1.2 L2-error estimates 222
7.1.3 H1 error estimates 225
7.1.4 Maximum-norm error estimates 226
7.2 Parabolic optimal control problems 227
7.2.1 Crank-Nicolson finite volume scheme 228
7.2.2 Error estimates of CN-FVEM 235
7.3 Hyperbolic optimal control problems 239
7.3.1 Finite volume element methods 240
7.3.2 A priori error estimates 241
7.4 Numerical examples 249
7.4.1 Elliptic optimal control problems 249
7.4.2 Parabolic optimal control problems 251
7.4.3 Hyperbolic optimal control problems 253
Chapter 8 Variational discretization methods for optimal control problems 256
8.1 Variational discretization 256
8.1.1 Variati
内容摘要《**控制问题高效算法理论（英文版）》主要介绍了几类**控制问题的高效算法，包括了椭圆**控制问题、抛物**控制问题、双曲**控制问题、四阶**控制问题等新近热门领域，结合了作者本人在**控制问题方面的研究成果，并根据作者对有限元方法、变分离散方法、混合有限元方法、有限体积法和谱方法的理解和研究生教学要求，全面、客观的评价了这几类**控制问题的数值计算方法，并列举了很多数值算例，阐述了许多新的学术观点，具有较大的学术价值。
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