偏微分方程最优控制的自适应有限元方法
2008-1
科学出版社
Wenbin Liu 等著
199
The main idea used in error analysis is to first combine convex analysis and interpolation error estimations of suitable interpolators, whichmuch depend on the structure of the control constraints, in order to derive error estimates for the control via the variational inequalities in the optimality conditions, and then to apply the standard techniques for deriving error estimates for the state equations.
Chapter 1 Introduction 1.1 Examples of optimal control for elliptic systems 1.2 Examples of optimal control for evolution equations 1.3 Examples of optimal control for flow 1.4 Shape optimal controlChapter 2 Existence and Optimality Conditions of Optimal Control 2.1 Existence of optimal control 2.2 Optimality conditions of optimal controlChapter 3 Finite Element Approximation of Optimal Control 3.1 Finite element schemes for elliptic optimal control 3.2 Mixed finite element schemes for elliptic optimal control 3.3 Optimal control governed by Stokes equations 3.4 Finite element method for boundary controlChapter 4 A Priori Error Estimates for Optimal Control (I) 4.1 A priori error estimates for distributed elliptic control 4.2 A priori error estimates for elliptic boundary control 4.3 Superconvergence analysis for distributed elliptic control 4.4 Further developments on superconvergenceChapter 5 A Priori Error Estimates for Optimal Control (II) 5.1 A priori error estimates of mixed FEM for elliptic control 5.2 Superconvergence of mixed FEM for elliptic control 5.3 A priori error estimates for Stokes control 5.4 Superconvergence for Stokes controlChapter 6 Adaptivity Finite Element Method for Optimal Control 6.1 Adaptive finite element method for elliptic equations 6.2 Adaptive finite element method for optimal controlChapter 7 A Posteriori Error Estimates for Optimal Control 7.1 A posteriori error estimates for distributed control 7.2 A posteriori error estimates with lower and upper bounds 7.3 Sharp a posteriori error estimates for constraints of obstacle type 7.4 A posteriori error estimates in L2-norm 7.5 A posteriori error estimates for nonlinear control 7.6 A posteriori error estimates for boundary controlChapter 8 Numerical Computations of Optimal Control 8.1 Numerical solutions of optimal control 8.2 A preconditioned projection algorithm 8.3 Numerical Experiments 8.4 Appendix-L2-Projectors to some closed convex subsetsChapter 9 Recovery Based a Posteriori Error 9.1 Equivalence of a posteriori error estimatiors of recovery type 9.2 Asymptotical exactness of a poteriori error estimators of recovery typeChapter 10 Adaptive mixed finite element method for optimal control 10.1 A posteriori error estimates for elliptic control 10.2 A posteriori error estimates for stokes controlBibliography
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