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

共 22 条

[1] [Anonymous], 2007, FENICS
[2] Error estimates for the numerical approximation of a semilinear elliptic control problem
Arada, N
Casas, E
Tröltzsch, F
[J]. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2002, 23 (02) : 201 - 229
[3] Brenner S. C., 2007, MATH THEORY FINITE E
[4] Carstensen C, 1999, RAIRO-MATH MODEL NUM, V33, P1187
[5] Casas E, 2003, INT FED INFO PROC, V121, P89
[6] CASAS E., SIAM J OPTI IN PRESS
[7] Error estimates for the numerical approximation of Neumann control problems
Casas, Eduardo
Mateos, Mariano
[J]. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2008, 39 (03) : 265 - 295
[8] Error estimates for the numerical approximation of Dirichlet boundary control for semilinear elliptic equations
Casas, Eduardo
Raymond, Jean-Pierre
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2006, 45 (05) : 1586 - 1611
[9] Using piecewise linear functions in the numerical approximation of semilinear elliptic control problems
Casas, Eduardo
[J]. ADVANCES IN COMPUTATIONAL MATHEMATICS, 2007, 26 (1-3) : 137 - 153
[10] Casas E, 2002, COMPUT APPL MATH, V21, P67

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