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Semi-discrete a priori error analysis for the optimal control of the unsteady Navier–Stokes equations with variational multiscale stabilization

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  • Yılmaz, Fikriye

Abstract

In this work, the optimal control problems of the unsteady Navier–Stokes equations with variational multiscale stabilization (VMS) are considered. At first, the first order continuous optimality conditions are obtained. Since the adjoint equation of the Navier–Stokes problem is a convection diffusion type system, then the same stabilization is applied to it. Semi discrete a priori error estimates are obtained for the state, adjoint state and control variables. Crank–Nicholson time discretization is used to get the fully discrete scheme. Numerical examples verify the theoretical findings and show the efficiency of the stabilization for higher Reynolds number.

Suggested Citation

  • Yılmaz, Fikriye, 2016. "Semi-discrete a priori error analysis for the optimal control of the unsteady Navier–Stokes equations with variational multiscale stabilization," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 127-142.
    • Handle: RePEc:eee:apmaco:v:276:y:2016:i:c:p:127-142
    DOI: 10.1016/j.amc.2015.11.092
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    References listed on IDEAS

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    1. Gang Chen & Minfu Feng, 2014. "Subgrid scale eddy viscosity finite element method on optimal control of system governed by unsteady Oseen equations," Computational Optimization and Applications, Springer, vol. 58(3), pages 679-705, July.
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    Cited by:

    1. Haçat, Gülnur & Yılmaz, Fikriye & Çıbık, Aytekin & Kaya, Songül, 2022. "Error estimates for the optimal control of Navier-Stokes equations using curvature based stabilization," Applied Mathematics and Computation, Elsevier, vol. 430(C).

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