Finite element error estimates for Neumann boundary control problems on graded meshes

被引：34

作者：

Apel, Thomas ^{[1
]}

Pfefferer, Johannes ^{[1
]}

Roesch, Arnd ^{[2
]}

机构：

[1] Univ Bundeswehr Munchen, D-85579 Neubiberg, Germany

[2] Univ Duisburg Essen, D-47057 Duisburg, Germany

来源：

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS | 2012年 / 52卷 / 01期

基金：

奥地利科学基金会;

关键词：

Linear-quadratic elliptic optimal control problem; Boundary control; A-priori error estimates; Mesh grading; Postprocessing; Variational discretization; NUMERICAL APPROXIMATION; VARIATIONAL DISCRETIZATION;

D O I：

10.1007/s10589-011-9427-x

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：

A specific elliptic linear-quadratic optimal control problem with Neumann boundary control is investigated. The control has to fulfil inequality constraints. The domain is assumed to be polygonal with reentrant corners. The asymptotic behaviour of two approaches to compute the optimal control is discussed. In the first the piecewise constant approximations of the optimal control are improved by a postprocessing step. In the second the control is not discretized; instead the first order optimality condition is used to determine an approximation of the optimal control. Although the quality of both approximations is in general affected by corner singularities a convergence order of 3/2 can be proven provided that the mesh is sufficiently graded.

引用

页码：3 / 28

页数：26

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