Free Access
Issue
ESAIM: COCV
Volume 18, Number 4, October-December 2012
Page(s) 987 - 1004
DOI https://doi.org/10.1051/cocv/2011201
Published online 16 January 2012
  1. F. Abraham, M. Behr and M. Heinkenschloss, The effect of stabilization in finite element methods for the optimal boundary control of the Oseen equations. Finite Elem. Anal. Des. 41 (2004) 229–251. [CrossRef]
  2. R. Becker and M. Braack, A two-level stabilization scheme for the Navier-Stokes equations, in Numerical Mathematics and Advanced Applications, ENUMATH 2003. edited by, M. Feistauer et al., Springer (2004) 123–130.
  3. R. Becker and B. Vexler, Optimal control of the convection-diffusion equation using stabilized finite element methods. Numer. Math. 106 (2007) 349–367. [CrossRef] [MathSciNet]
  4. M. Braack, Optimal control in fluid mechanics by finite elements with symmetric stabilization. SIAM J. Control Optim. 48 (2009) 672–687. [CrossRef] [MathSciNet]
  5. M. Braack and E. Burman, Local projection stabilization for the Oseen problem and its interpretation as a variational multiscale method. SIAM J. Numer. Anal. 43 (2006) 2544–2566. [CrossRef] [MathSciNet]
  6. M. Braack, E. Burman, V. John and G. Lube, Stabilized finite element methods for the generalized Oseen problem. Comput. Methods Appl. Mech. Engrg. 196 (2007) 853–866. [CrossRef] [MathSciNet]
  7. A.N. Brooks and T.J.R. Hughes, Streamline upwind Petrov-Galerkin formulation for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Comput. Methods Appl. Mech. Engrg. 32 (1982) 199–259. [CrossRef] [MathSciNet]
  8. S.S. Collis and M. Heinkenschloss, Analysis of the streamline upwind/Petrov Galerkin method applied to the solution of optimal control problems. Technical report 02-01, Rice University, Houston, TX (2002).
  9. L. Dedé and A. Quarteroni, Optimal control and numercal adaptivity for advection-diffusion equations. ESIAM : M2AN 39 (2005) 1019–1040. [CrossRef] [EDP Sciences]
  10. V. Girault and P.-A. Raviart, Finite Elements for the Navier Stokes Equations. Springer, Berlin (1986).
  11. M. Heinkenschloss and D. Leykekhman, Local error estimates for SUPG solutions of advection-dominated elliptic linear-quadratic optimal control problems. SIAM J. Numer. Anal. 47 (2010) 4607–4638. [CrossRef] [MathSciNet]
  12. M. Hinze, N. Yan and Z. Zhou, Variational discretization for optimal control governed by convection dominated diffusion equations. J. Comput. Math. 27 (2009) 237–253.
  13. C. Johnson and J. Saranen, Streamline diffusion methods for the incompressible Euler and Navier-Stokes equations. Math. Comput. 47 (1986) 1–18. [CrossRef]
  14. G. Lube and G. Rapin, Residual-based stabilized higher-order FEM for a generalized Oseen problem. Math. Models Methods Appl. Sci. 16 (2006) 949–966. [CrossRef]
  15. G. Lube and G. Rapin, Residual-based stabilized higher-order FEM for a generalized Oseen problem. Math. Models Methods Appl. Sci. 16 (2006) 949–966. [CrossRef]
  16. G. Lube and B. Tews, Optimal control of singularly perturb advection-diffusion-reaction problems. Math. Models Appl. Sci. 20 (2010) 1–21. [CrossRef]
  17. G. Matthies, P. Skrzypacz and L. Tobiska, A unified convergence analysis for local projection stabilisations applied ro the Oseen problem. ESAIM : M2AN 41 (2007) 713–742. [CrossRef] [EDP Sciences]
  18. N. Yan and Z. Zhou, A priori and a posteriori error estimates of streamline diffusion finite element method for optimal control problems governed by convection dominated diffusion equation. NMTMA 1 (2008) 297–320.
  19. N. Yan and Z. Zhou, A priori and a posteriori error analysis of edge stabilization Galerkin method for the optimal control problem governed by convection dominated diffusion equation. J. Comput. Appl. Math. 223 (2009) 198–217. [CrossRef]

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