A priori error analysis of the petrov-galerkin crank-nicolson scheme for parabolic optimal control problems

Dominik Meidner, Boris Vexler

Research output: Contribution to journalArticlepeer-review

34 Scopus citations

Abstract

In this paper, a finite element discretization of an optimal control problem governed by the heat equation is considered. The temporal discretization is based on a Petrov-Galerkin variant of the Crank-Nicolson scheme, whereas the spatial discretization employs usual conforming finite elements. With a suitable postprocessing step, a discrete solution is obtained for which error estimates of optimal order are proven. A numerical result is presented for illustrating the theoretical findings.

Original languageEnglish
Pages (from-to)2183-2211
Number of pages29
JournalSIAM Journal on Control and Optimization
Volume49
Issue number5
DOIs
StatePublished - 2011

Keywords

  • Control constraints
  • Crank-Nicolson scheme
  • Error estimates
  • Finite elements
  • Heat equation
  • Optimal control

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