Comparison of the reduced-basis and POD a posteriori error estimators for an elliptic linear-quadratic optimal control problem

被引：21

作者：

Tonn, Timo ^{[2
]}

Urban, K. ^{[2
]}

Volkwein, S. ^{[1
]}

机构：

[1] Univ Konstanz, Fachbereich Math & Stat, Univ Str 10, D-78457 Constance, Germany

[2] Univ Ulm, Inst Numer Math, D-89069 Ulm, Germany

来源：

MATHEMATICAL AND COMPUTER MODELLING OF DYNAMICAL SYSTEMS | 2011年 / 17卷 / 04期

基金：

奥地利科学基金会;

关键词：

optimal control; a posteriori error estimate; proper orthogonal decomposition; reduced-basis method; Helmholtz equation;

D O I：

10.1080/13873954.2011.547678

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

In this article, a linear-quadratic optimal control problem governed by the Helmholtz equation is considered. For the computation of suboptimal solutions, two different model reduction techniques are compared: the reduced-basis method and proper orthogonal decomposition. By an a posteriori error estimator for the optimal control problem, the accuracy of the suboptimal solutions is ensured. The efficiency of both model reduction approaches is illustrated by a numerical example for the stationary Helmholtz equation.

引用

页码：355 / 369

页数：15

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