OPTIMALITY CONDITIONS AND ERROR ANALYSIS OF SEMILINEAR ELLIPTIC CONTROL PROBLEMS WITH L1 COST FUNCTIONAL

被引：81

作者：

Casas, Eduardo ^{[1
]}

Herzog, Roland ^{[2
]}

Wachsmuth, Gerd ^{[2
]}

机构：

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

[2] Tech Univ Chemnitz, Fac Math, D-09126 Chemnitz, Germany

来源：

SIAM JOURNAL ON OPTIMIZATION | 2012年 / 22卷 / 03期

关键词：

optimal control of partial differential equations; nondifferentiable objective; sparse controls; finite element discretization; a priori error estimates; NUMERICAL APPROXIMATION; CONVERGENCE;

D O I：

10.1137/110834366

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Semilinear elliptic optimal control problems involving the L-1 norm of the control in the objective are considered. Necessary and sufficient second-order optimality conditions are derived. A priori finite element error estimates for piecewise constant discretizations for the control and piecewise linear discretizations of the state are shown. Error estimates for the variational discretization of the problem in the sense of [M. Hinze, Comput. Optim. Appl., 30 (2005), pp. 45-61] are also obtained. Numerical experiments confirm the convergence rates.

引用

页码：795 / 820

页数：26

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