A posteriori error estimation for a PDE-constrained optimization problem involving the generalized oseen equations

Alejandro Allendes, Enrique Otarola, Richard Rankin

Research output: Journal PublicationArticlepeer-review

1 Citation (Scopus)
4 Downloads (Pure)

Abstract

We derive globally reliable a posteriori error estimators for a linear-quadratic optimal control problem involving the generalized Oseen equations as state equations; control constraints are also considered. The corresponding local error indicators are locally efficient. The assumptions under which we perform the analysis are such that they can be satisfied for a wide variety of stabilized finite element methods as well as for standard finite element methods. When stabilized methods are considered, no a priori relation between the stabilization terms for the state and adjoint equations is required. If a lower bound for the inf-sup constant is available, a posteriori error estimators that are fully computable and provide guaranteed upper bounds on the norm of the error can be obtained. We illustrate the theory with numerical examples.

Original languageEnglish
Pages (from-to)A2200-A2233
JournalSIAM Journal of Scientific Computing
Volume40
Issue number4
DOIs
Publication statusPublished - 2018

Keywords

  • A posteriori error estimators
  • Brinkman equations
  • Generalized Oseen equations
  • Linear-quadratic optimal control problems
  • Stabilized adaptive finite element methods
  • Stokes equations

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'A posteriori error estimation for a PDE-constrained optimization problem involving the generalized oseen equations'. Together they form a unique fingerprint.

Cite this