A posteriori error estimation in PDE-constrained optimization with pointwise inequality constraints

Rolf Rannacher; Boris Vexler; Winnifried Wollner

doi:10.1007/978-3-0348-0133-1

A posteriori error estimation in PDE-constrained optimization with pointwise inequality constraints

Rolf Rannacher, Boris Vexler, Winnifried Wollner

Chair of Optimal Control

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

7 Scopus citations

Abstract

This article summarizes several recent results on goal-oriented error estimation and mesh adaptation for the solution of elliptic PDE-constrained optimization problems with additional inequality constraints. The first part is devoted to the control constrained case. Then some emphasis is given to pointwise inequality constraints on the state variable and on its gradient. In the last part of the article regularization techniques for state constraints are considered and the question is addressed, how the regularization parameter can adaptively be linked to the discretization error.

Original language	English
Title of host publication	Constrained Optimization and Optimal Control for Partial Differential Equations
Publisher	Springer Basel
Pages	349-373
Number of pages	25
ISBN (Electronic)	9783034801331
ISBN (Print)	9783034801324
DOIs	https://doi.org/10.1007/978-3-0348-0133-1
State	Published - 1 Jan 2012

Keywords

Adaptive finite elements
Adaptivity
Control and state constraints
Goal oriented error estimation
PDE-constrained optimization
regularization

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10.1007/978-3-0348-0133-1

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ER -

A posteriori error estimation in PDE-constrained optimization with pointwise inequality constraints

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