Error estimates for the numerical approximation of a semilinear elliptic control problem

被引：226

作者：

Arada, N ^{[1
]}

Casas, E

Tröltzsch, F

机构：

[1] Tech Univ Chemnitz, Fak Math, D-09107 Chemnitz, Germany

[2] Univ Cantabria, Dept Matemat Aplicada & Ciencias Computac, E-39005 Santander, Spain

[3] Tech Univ Berlin, Inst Math, D-10623 Berlin, Germany

来源：

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS | 2002年 / 23卷 / 02期

关键词：

distributed control; semilinear elliptic equation; numerical approximation; finite element method; error estimates;

D O I：

10.1023/A:1020576801966

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

We study the numerical approximation of distributed nonlinear optimal control problems governed by semilinear elliptic partial differential equations with pointwise constraints on the control. Our main result are error estimates for optimal controls in the maximum norm. Characterization results are stated for optimal and discretized optimal control. Moreover, the uniform convergence of discretized controls to optimal controls is proven under natural assumptions.

引用

页码：201 / 229

页数：29

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