A general theorem on error estimates with application to a quasilinear elliptic optimal control problem

被引：25

作者：

Casas, Eduardo ^{[2
]}

Troeltzsch, Fredi ^{[1
]}

机构：

[1] Tech Univ Berlin, Inst Math, D-10623 Berlin, Germany

[2] Univ Cantabria, Dept Matemat Aplicada & Ciencias Computac, ETSI Ind Telecomunicac, E-39005 Santander, Spain

来源：

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS | 2012年 / 53卷 / 01期

关键词：

Quasilinear elliptic equations; Optimal control problems; Optimality conditions; Finite element approximation; Error estimates; NUMERICAL APPROXIMATION; CONSTRAINTS; EQUATIONS;

D O I：

10.1007/s10589-011-9453-8

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：

A theorem on error estimates for smooth nonlinear programming problems in Banach spaces is proved that can be used to derive optimal error estimates for optimal control problems. This theorem is applied to a class of optimal control problems for quasilinear elliptic equations. The state equation is approximated by a finite element scheme, while different discretization methods are used for the control functions. The distance of locally optimal controls to their discrete approximations is estimated.

引用

页码：173 / 206

页数：34

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