最优控制问题高效高精度算法
本书特色
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陈艳萍、鲁祖亮编写的《*优控制问题高效高精 度算法（英文版）（精）》主要介绍了几类*优控制问题 的高效算法，包括了椭圆*优控制问题、抛物*优控 制问题、双曲*优控制问题、四阶*优控制问题等新 近热门领域，结合了作者本人在*优控制问题方面的 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*优控制 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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目录
chapter 1 introductionchapter 2 some preliminaries 2.1 sobolevspaces 2.2 finite element methods for elliptic equations 2.2.1 a priori error estimates 2.2.2 a posteriori error estimates 2.2.3 superconvergence 2.3 mixed finite element methods 2.3.1 elliptic equations 2.3.2 parabolic equations 2.3.3 hyperbolic equations 2.4 optimal control problems 2.4.1 backgrounds and motivations 2.4.2 some typical examples 2.4.3 optimality conditionschapter 3 finite element methods for optimal control problems 3.1 elliptic optimal control problems 3.1.1 distributed elliptic optimal control problems 3.1.2 finite element diseretization 3.1.3 m posterinri error estimates 3.2 parabolic optimal control problems 3.2.1 fully discrete finite element approximation 3.22 intermediate error estimates 3.2.3 superconvergence 3.3 optimal control problems with oscillating coefficients 3.3.1 finite element scheme 3.32 multiscale finite element scheme 3.3.3 homogenization theory and related estimates 3.3.4 convergence analysis 3.4 recovery a posteriori error estimates 3.4.1 fully discrete finite element scheme 3.4.2 error estimates of intermediate variables 3.4.3 superconvergence 3.4a a posteriori error estimates 3.5 numerical examples 3.5.1 parabolic optimal control problems 3.5.2 recovery a posteriori error estimateschapter 4 a priori error estimates of mixed finite element methods ~. 4,1 elliptic optimal control problems & 1.1 mixed finite element scheme 4,1.2 a priori error estimates 4.2 parabolic optimal control problems 4.2.1 mixed finite element discretization 4.2.2 mixed method projection 4.2.3 intermediate error estimates 4.2.4 a priori error estimates 4.3 hyperbolic optimal control problems 4.3.1 mixed finite element methods 4.32 a priori error estimates 4.4 fourth order optimal control problems 4.4.1 mixed finite element scheme 4.4.2 l2-error estimates 4.43 l~-error estimates 4.5 nonlinear optimal control problems 4.5.1 mixed finite element discretization 4.5.2 error estimates 4.6 numerical examples 4.6.1 elliptic optimal control problems 4.6.2 fourth order optimal control problemschapter 5 a posteriori error estimates of mixed finite element methods- 5.1 elliptic optimal control problems 5.1.1 mixed finite element discretization 5.1.2 a posteriori error estimates for control variable 5.1.3 a posteriori error estimates for state variables 5.2 parabolic optimal control problems 52.1 mixed finite element approximation 5.2.2 a posteriori error estimates 5.3 hyperbolic optimal control problems 5.3.1 intermediate error estimates 5.3.2 a posteriori error estimates for control variable 5.33 a posteriori error estimates for state variables 5a nonlinear optimal control problems 5.4,1 mixed finite element discretization 5.4.2 intermediate error estimates 5.43 a posteriofi error estimateschapter 6 superconvergence of mixed finite element methods 6.1 elliptic optimal control problems 6.1,1 recovery operator 6.1.2 superconvergence property 6.2 parabolic optimal control problems 62.1 superconvergence for the intermediate errors 6.2.2 superconvergence 6.3 hyperbolic optimal control problems 6.3.1 superconvergence property 6.32 superconvergence for the control variable 6.4 nonlinear optimal control problems 6.4.1 supereonvergence for the intermediate errors 6.4.2 global superconvergence 6.4.3 h-t-error estimates 6.5 numerical examples 6.5,1 elliptic optimal control problems 6.52 nonlinear optimal control problemschapter 7 finite volume element methods for optimal control problems 7.1 elliptic optimal control problems 7.1.1 finite volume element methods 7.12 l2-error estimates 7.1,3 hj error estimates 7.1.4 maximum-norm error estimates 7.2 parabolic optimal control problems 7.2.1 crank-nicolson finite volume scheme 7.2,2 error estimates of cn-fvem 7.3 hyperbolic optimal control problems 7.3.1 finite volume element methods 7.32 a priori error estimates 7.4 numerical examples 7.4.1 elliptic optimal control problems 7.4.2 parabolic optimal control problems 7.4.3 hyperbolic optimal control problemschapter 8 variational diseretization methods for optimal control problems ~ ~ ~ 8.1 variational discretization 8.1.1 variational discretization scbeme 8.122 a priori error estimates 8.1.3 a posteriori error estimates 8~2 mixed variational discretization 82.1 mixed finite element approximation and variational discretization 82.2 a priori error estimates for semi-discrete scheme 82.3 a priori error estimates for fully discrete scheme 8.3 numerical examples 8.3.1 variational discretizatinn 8.3.2 mixed variational discretizationchapter 9 legendre-galerkin spectral methods for optimal control problems. 9.1 elliptic optimal control problems 9.1 1 legendre-galerkin spectral approximation 9.1.2 regularity of the optimal control 9.1.3 a priori error estimates 9.1.4 a posteriori error estimates 9.1.5 the hp spectral element methods 9.2 parabolic optimal control problems 9.2.1 legendre-galerkin spectral methods 9.2.2 a priori error estimates 9.2.3 a posteriori error estimates 9.3 optimal control problems governed by stokes equations 9.3.1 legendre-galerkin spectral approximation 9.3.2 a priori error estimates 9.3.3 a posteriori error estimates 9.4 optimal control problems with integral state and control constraints 9.4.1 legendre-galerkin spectral scheme 9.4.2 a priori error estimates 9.4.3 a posteriori error estimates 9.5 numerical examples 9.5.1 elliptic optimal control problems 9.5.2 optimal control problems governed by stokes equations 9.5.3 optimal control problems with integral state and control constraintsbibliographyindex
封面
书名:最优控制问题高效高精度算法
作者:陈艳萍
页数:385
定价:¥128.0
出版社:科学出版社
出版日期:2015-12-01
ISBN:9787030463951
PDF电子书大小:40MB 高清扫描完整版