Numerical resolution of optimal control problem for the in-stationary Navier–Stokes equations

References

[1] R. Agroum, S. Mani Aouadi, C. Bernardi and J. Satouri, Spectral discretization of the Navier–Stokes equations coupled with the heat equation, ESAIM Math. Model. Numer. Anal. 49 (2015), no. 3, 621–639. 10.1051/m2an/2014049Search in Google Scholar

[2] C. Bernardi and Y. Maday, Spectral methods, Handbook of Numerical Analysis, North-Holland, Amsterdam (1997), 209–485. 10.1016/S1570-8659(97)80003-8Search in Google Scholar

[3] M. Böhm, M. A. Demetriou, S. Reich and I. G. Rosen, Model reference adaptive control of distributed parameter systems, SIAM J. Control Optim. 36 (1998), no. 1, 33–81. 10.1137/S0363012995279717Search in Google Scholar

[4] D. Bresch-Pietri and M. Krstic, Output-feedback adaptive control of a wave PDE with boundary anti-damping, Automatica J. IFAC 50 (2014), no. 5, 1407–1415. 10.1016/j.automatica.2014.02.040Search in Google Scholar

[5] F. Brezzi, J. Rappaz and P.-A. Raviart, Finite-dimensional approximation of nonlinear problems. I. Branches of nonsingular solutions, Numer. Math. 36 (1980/81), no. 1, 1–25. 10.1007/BF01395985Search in Google Scholar

[6] J. C. De Los Reyes and R. Griesse, State-constrained optimal control of the three-dimensional stationary Navier–Stokes equations, J. Math. Anal. Appl. 343 (2008), no. 1, 257–272. 10.1016/j.jmaa.2008.01.029Search in Google Scholar

[7] A. V. Fursikov, M. D. Gunzburger and L. S. Hou, Boundary value problems and optimal boundary control for the Navier–Stokes system: The two-dimensional case, SIAM J. Control Optim. 36 (1998), no. 3, 852–894. 10.1137/S0363012994273374Search in Google Scholar

[8] A. V. Fursikov, M. D. Gunzburger and L. S. Hou, Optimal boundary control for the evolutionary Navier-Stokes system: The three-dimensional case, SIAM J. Control Optim. 43 (2005), no. 6, 2191–2232. 10.1137/S0363012904400805Search in Google Scholar

[9] V. Girault and P.-A. Raviart, Finite Element Approximation of the Navier–Stokes Equations, Lecture Notes in Math. 749, Springer, Berlin, 1979. 10.1007/BFb0063447Search in Google Scholar

[10] V. Girault and P.-A. Raviart, An analysis of upwind schemes for the Navier–Stokes equations, SIAM J. Numer. Anal. 19 (1982), no. 2, 312–333. 10.1137/0719019Search in Google Scholar

[11] E. Hopf, On non-linear partial differential equations, Lecture Series of the Symposium on Partial Differential Equations (Berkeley 1955), University of Kansas, Lawrence (1957), 1–31. Search in Google Scholar

[12] C. Jia, A note on the model reference adaptive control of linear parabolic systems with constant coefficients, J. Syst. Sci. Complex. 24 (2011), no. 6, 1110–1117. 10.1007/s11424-011-0042-9Search in Google Scholar

[13] I. Neitzel and F. Tröltzsch, On regularization methods for the numerical solution of parabolic control problems with pointwise state constraints, ESAIM Control Optim. Calc. Var. 15 (2009), no. 2, 426–453. 10.1051/cocv:2008038Search in Google Scholar

[14] M. A. Younes and S. Abidi, The Navier–Stokes problem in the velocity-pressure formulation, Int. J. Appl. Math. 24 (2011), no. 3, 469–477. Search in Google Scholar