Approximation of sparse controls in semilinear equations by piecewise linear functions

被引：32

作者：

Casas, Eduardo ^{[2
]}

Herzog, Roland ^{[1
]}

Wachsmuth, Gerd ^{[1
]}

机构：

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

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

来源：

NUMERISCHE MATHEMATIK | 2012年 / 122卷 / 04期

关键词：

ELLIPTIC CONTROL-PROBLEMS; FINITE-ELEMENT-METHOD; NUMERICAL APPROXIMATION; ERROR ANALYSIS;

D O I：

10.1007/s00211-012-0475-7

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 norm of the control in the objective are considered. A priori finite element error estimates for piecewise linear discretizations for the control and the state are proved. These are obtained by a new technique based on an appropriate discretization of the objective function. Numerical experiments confirm the convergence rates.

引用

页码：645 / 669

页数：25

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