Third order convergent time discretization for parabolic optimal control problems with control constraints

被引:6
|
作者
Springer, Andreas [1 ]
Vexler, Boris [1 ]
机构
[1] Tech Univ Munich, Fak Math, Lehrstuhl Optimale Steuerung, D-85748 Garching, Germany
基金
奥地利科学基金会;
关键词
Optimal control; Heat equation; Control constraints; Discontinuous Galerkin time stepping; Error estimates; Post-processing; Variational control discretization; FINITE-ELEMENT DISCRETIZATION; PRIORI ERROR ANALYSIS; SUPERCONVERGENCE PROPERTIES; SPACE; STRATEGY;
D O I
10.1007/s10589-013-9580-5
中图分类号
C93 [管理学]; O22 [运筹学];
学科分类号
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要
We consider a priori error analysis for a discretization of a linear quadratic parabolic optimal control problem with box constraints on the time-dependent control variable. For such problems one can show that a time-discrete solution with second order convergence can be obtained by a first order discontinuous Galerkin time discretization for the state variable and either the variational discretization approach or a post-processing strategy for the control variable. Here, by combining the two approaches for the control variable, we demonstrate that almost third order convergence with respect to the size of the time steps can be achieved.
引用
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页码:205 / 240
页数:36
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