chapter 1 introduction chapter 2 some preliminaries 2.1 sobolev spaces 2.2 finite element methods for elliptic equations 2.2.1 a priori error estimates 2.2.2 a teriori 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 conditions chapter 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 discretization 3.1.3 a teriori error estimates 3.2 parabolic optimal control problems 3.2.1 fully discrete finite element appromation 3.2.2 intermediate error estimates 3.2.3 superconvergence 3.3 optimal control problems with oscillating coefficients 3.3.1 finite element scheme 3.3.2 multiscale finite element scheme 3.3.3 homogenization theory and related estimates 3.3.4 convergence analysis 3.4 recovery a teriori error estimates 3.4.1 fully discrete finite element scheme 3.4.2 error estimates ofintermediate variables 3.4.3 superconvergence 3.4.4 a teriori error estimates 3.5 numerical examples 3.5.1 parabolic optimal control problems 3.5.2 recovery a teriori error estimates chapter 4 a priori error estimates of mixed finite element methods 4.1 elliptic optimal control problems 4.1.1 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 4.3.2 a priori error estimates 4.4 fourth order optimal control problems 4.4.1 mixed finite element scheme 4.4.2 l2-error estimates 4.4.3 l ∞-error estimates 4.5 nonlmear 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 problems chapter 5 a teriori error estimates of mixed finite element methods 5.1 elliptic optimal control problems 5.1.1 mixed finite element discretization 5.1.2 a teriori error estimates for control variable 5.1.3 a teriori error estimates for state variables 5.2 parabolic optimal control problems 5.2.1 mixed finite element appromation 5.2.2 a teriori error estimates 5.3 hyperbolic optimal control problems 5.3.1 intermediate error estimates 5.3.2 a teriori error estimates for control variable 5.3.3 a teriori error estimates for state variables 5.4 nonlinear optimal control problems 5.4.1 mixed finite element discretization 5.4.2 intermediate error estimates 5.4.3 a teriori error estimates chapter 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 6.2.1 superconvergence for the intermediate errors 6.2.2 superconvergence 6.3 hyperbolic optimal control problems 6.3.1 superconvergence property 6.3.2 superconvergence for the control variable 6.4 nonlinear optimal control problems 6.4.1 superconvergence for the intermediate errors 6.4.2 global superconvergence 6.4.3 h—1—error estimates 6.5 numerical examples 6.5.1 elliptic optimal control problems 6.5.2 nonlinear optimal control problems chapter 7 finite volume element methods for optimal control problems 7.1 elliptic optimal control problems 7.1.1 finite volume element methods 7.1.2 l2—error estimates 7.1.3 h1 error estimates 7.1.4 mamum—norm error estimates 7.2 parabolic optimal control problems 7.2.1 crank—nicolson finite volume scheme 7.2.2 error estimates of —fvem 7.3 hyperbolic optimal control problems 7.3.1 finite volume element methods 7.3.2 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 problems chapter 8 variational discretization methods for optimal control problems 8.1 variational discretization 8.1.1 variational discretization scheme 8.1.2 a priori error estimates 8.1.3 a teriori error estimates 8.2 mixed variational discretization 8.2.1 mixed finite element appromation and variational discretization 8.2.2 a priori error estimates for semi—discrete scheme 8.2.3 a priori error estimates for fully discrete scheme 8.3 numerical examples 8.3.1 variational discretization 8.3.2 mixed variational discretization chapter 9 legendre—galerkin spectral methods for optimal control problems 9.1 elliptic optimal control problems 9.1.1 legendre—galerkin spectral appromation 9.1.2 regularity of the optimal control 9.1.3 a priori error estimates 9.1.4 a teriori 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 teriori error estimates 9.3 optimal control problems governed by stokes equations 9.3.1 legendre—galerkin spectral appromation 9.3.2 a priori error estimates 9.3.3 a teriori 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 teriori 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 constraints bibliography index
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