Implementation and analysis of multigrid schemes with finite elements for elliptic optimal control problems

被引：35

作者：

Lass, O. ^{[1
]}

Vallejos, M. ^{[1
,2
]}

Borzi, A. ^{[1
,3
]}

Douglas, C. C. ^{[4
]}

机构：

[1] Karl Franzens Univ Graz, Inst Math & Wissensch Rechnen, A-8010 Graz, Austria

[2] Univ Philippines, Coll Sci, Inst Math, Diliman, Philippines

[3] Univ Sannio, Dipartimento & Fac Ingn, I-82100 Benevento, Italy

[4] Univ Wyoming, Dept Math, Laramie, WY 82071 USA

来源：

COMPUTING | 2009年 / 84卷 / 1-2期

基金：

美国国家科学基金会; 奥地利科学基金会;

关键词：

Elliptic optimal control problem; Finite elements; Multigrid method; BOUNDARY-VALUE-PROBLEMS; OPTIMIZATION; ALGORITHMS; CONVERGENCE; SPACES;

D O I：

10.1007/s00607-008-0024-5

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

The detailed implementation and analysis of a finite element multigrid scheme for the solution of elliptic optimal control problems is presented. A particular focus is in the definition of smoothing strategies for the case of constrained control problems. For this setting, convergence of the multigrid scheme is discussed based on the BPX framework. Results of numerical experiments are reported to illustrate and validate the optimal efficiency and robustness of the performance of the present multigrid strategy.

引用

页码：27 / 48

页数：22

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