ERROR ANALYSIS FOR A FINITE ELEMENT APPROXIMATION OF ELLIPTIC DIRICHLET BOUNDARY CONTROL PROBLEMS

被引：63

作者：

May, S. ^{[1
]}

Rannacher, R. ^{[2
]}

Vexler, B. ^{[3
]}

机构：

[1] NYU, Courant Inst Math Sci, New York, NY 10012 USA

[2] Heidelberg Univ, Inst Appl Math, D-69120 Heidelberg, Germany

[3] Tech Univ Munich, Ctr Math Sci, D-85747 Garching, Germany

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2013年 / 51卷 / 03期

基金：

奥地利科学基金会;

关键词：

Dirichlet boundary control; finite elements; a priori error estimates; LIPSCHITZ-DOMAINS; EQUATIONS; SPACES;

D O I：

10.1137/080735734

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We consider the Galerkin finite element approximation of an elliptic Dirichlet boundary control model problem governed by the Laplacian operator. The analytical setting of this problem uses L-2 controls and a "very weak" formulation of the state equation. However, the corresponding finite element approximation uses standard continuous trial and test functions. For this approximation, we derive a priori error estimates of optimal order, which are confirmed by numerical experiments. The proofs employ duality arguments and known results from the L-p error analysis for the finite element Dirichlet projection.

引用

页码：2585 / 2611

页数：27

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