Discretization estimates for an elliptic control problem
作者:
Viorel Arnǎutu,
Pekka Neittaanmäki,
期刊:
Numerical Functional Analysis and Optimization
(Taylor Available online 1998)
卷期:
Volume 19,
issue 5-6
页码: 431-464
ISSN:0163-0563
年代: 1998
DOI:10.1080/01630569808816838
出版商: Marcel Dekker, Inc.
关键词: optimal control;two-point BVP;elliptic equation;error estimates;finite element method;spectral method;49M15;65K10;65M60;65M70
数据来源: Taylor
摘要:
An optimal control problem governed by an elliptic equation written in variational form in an abstract functional framework is considered. The control is subject to restrictions. The optimality conditions are established and the Ritz-Galerkin discretization is introduced. If the error estimate corresponding to the elliptic equation is given as a function likewherehis the discretization parameter andis an integer, then the error estimates for the optimal control, for the optimal state and for the optimal value are obtained. These results are applied first for a Two-Point BVP and next for a 2D/3D elliptic problem as state equation. Next a spectral method is used in the discretization process. The estimates obtained in the abstract case are applied to a distributed control problem and to a boundary control problem.
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