Optimal control of the convection-diffusion equation using stabilized finite element methods

Roland Becker, Boris Vexler

Research output: Contribution to journalArticlepeer-review

134 Scopus citations

Abstract

In this paper we analyze the discretization of optimal control problems governed by convection-diffusion equations which are subject to pointwise control constraints. We present a stabilization scheme which leads to improved approximate solutions even on corse meshes in the convection dominated case. Moreover, the in general different approaches "optimize-then- discretize" and "discretize-then-optimize" coincide for the proposed discretization scheme. This allows for a symmetric optimality system at the discrete level and optimal order of convergence.

Original languageEnglish
Pages (from-to)349-367
Number of pages19
JournalNumerische Mathematik
Volume106
Issue number3
DOIs
StatePublished - May 2007
Externally publishedYes

Keywords

  • Error estimates
  • Optimal control
  • Pointwise inequality constraints
  • Stabilized finite elements

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