VARIATIONAL DISCRETIZATION OF PARABOLIC CONTROL PROBLEMS IN THE PRESENCE OF POINTWISE STATE CONSTRAINTS

被引：26

作者：

Deckelnick, Klaus ^{[1
]}

Hinze, Michael ^{[2
]}

机构：

[1] Otto von Guericke Univ, Inst Anal & Numer, Univ Pl 2, D-39106 Magdeburg, Germany

[2] Univ Hamburg, D-20146 Hamburg, Germany

来源：

JOURNAL OF COMPUTATIONAL MATHEMATICS | 2011年 / 29卷 / 01期

关键词：

Parabolic optimal control problem; State constraints; Error estimates; FINITE-ELEMENT APPROXIMATION; ELLIPTIC CONTROL-PROBLEMS; BOUNDARY CONTROL; CONVERGENCE;

D O I：

10.4208/jcm.1006-m3213

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a parabolic optimal control problem with pointwise state constraints. The optimization problem is approximated by a discrete control problem based on a discretization of the state equation by linear finite elements in space and a discontinuous Galerkin scheme in time. Error bounds for control and state are obtained both in two and three space dimensions. These bounds follow from uniform estimates for the discretization error of the state under natural regularity requirements.

引用

页码：1 / 15

页数：15

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