Adaptive finite elements for elliptic optimization problems with control constraints

B. Vexler, W. Wollner

Research output: Contribution to journalArticlepeer-review

77 Scopus citations

Abstract

In this paper we develop a posteriori error estimates for finite element discretization of elliptic optimization problems with pointwise inequality constraints on the control variable. We derive error estimators for assessing the discretization error with respect to the cost functional as well as with respect to a given quantity of interest. These error estimators provide quantitative information about the discretization error and guide an adaptive mesh refinement algorithm allowing for substantial saving in degrees of freedom. The behavior of the method is demonstrated on numerical examples.

Original languageEnglish
Pages (from-to)509-534
Number of pages26
JournalSIAM Journal on Control and Optimization
Volume47
Issue number1
DOIs
StatePublished - 2008
Externally publishedYes

Keywords

  • A posteriori error estimates
  • Finite element method
  • Mesh adaptivity
  • Optimal control
  • Pointwise inequality constraints
  • Quantity of interest

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