A posteriori error estimates for discontinuous galerkin time-stepping method for optimal control problems governed by parabolic equations

Wenbin Liu*, Heping Ma, Tao TANG, Ningning Yan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

56 Citations (Scopus)

Abstract

In this paper, we examine the discontinuous Galerkin (DG) finite element approximation to convex distributed optimal control problems governed by linear parabolic equations, where the discontinuous finite element method is used for the time discretization and the conforming finite element method is used for the space discretization. We derive a posteriori error estimates for both the state and the control approximation, assuming only that the underlying mesh in space is nondegenerate. For problems with control constraints of obstacle type, which are the kind most frequently met in applications, further improved error estimates are obtained.

Original languageEnglish
Pages (from-to)1032-1061
Number of pages30
JournalSIAM Journal on Numerical Analysis
Volume42
Issue number3
DOIs
Publication statusPublished - 2004

Scopus Subject Areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • A posteriori error analysis
  • Discontinuous galerkin method
  • Finite element approximation
  • Optimal control

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