Analysis and finite element error estimates for the velocity tracking problem for Stokes flows via a penalized formulation
ESAIM: Control, Optimisation and Calculus of Variations (2004)
- Volume: 10, Issue: 4, page 574-592
- ISSN: 1292-8119
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top- [1] R. Adams, Sobolev Spaces. Academic Press, New York (1975). Zbl0314.46030MR450957
- [2] K. Chrysafinos and L.S. Hou, Error estimates for semidiscrete finite element approximations of linear and semilinear parabolic equations under minimal regularity assumptions. SIAM J. Numer. Anal. 40 (2002) 282-306. Zbl1020.65068MR1921920
- [3] A. Fursikov,Optimal control of distributed systems. Theories and Applications. AMS Providence (2000). Zbl1027.93500
- [4] V. Girault and P.-A. Raviart, Finite Element Methods for Navier-Stokes. Springer-Verlag, New York (1986). Zbl0585.65077MR851383
- [5] M.D. Gunzburger, L.S. Hou and T. Svobodny, Analysis and finite element approximation of optimal control problems for the stationary Navier-Stokes equations with Dirichlet controls. ESAIM: M2AN 25 (1991) 711-748. Zbl0737.76045MR1135991
- [6] M.D. Gunzburger and S. Manservisi, The velocity tracking problem for Navier-Stokes flows with bounded distributed control. SIAM J. Control Optim. 37 (2000) 1913-1945. Zbl0938.35118MR1720145
- [7] M.D. Gunzburger and S. Manservisi, Analysis and approximation of the velocity tracking problem for Navier-Stokes flows with distributed control. SIAM J. Numer. Anal. 37 (2000) 1481-1512. Zbl0963.35150MR1759904
- [8] L.S. Hou, Error estimates for semidiscrete finite element approximation of the Stokes equations under minimal regularity assumptions. J. Sci. Comput. 16 (2001) 287-317. Zbl0996.76048MR1873285
- [9] L.S. Hou and S.S. Ravindran, A penalized Neumann control approach for solving an optimal Dirichlet control problem for the Navier-Stokes equations. SIAM J. Control Optim. 36 (1998) 1795-1814. Zbl0917.49003MR1632548
- [10] Jie Shen, On error estimates of the penalty method for unsteady Navier-Stokes equations. SIAM J. Numer. Anal. 32 (1995) 386-403. Zbl0822.35008MR1324294
- [11] R. Temam, Navier-Stokes equations. North-Holland, Amsterdam (1979). Zbl0426.35003MR603444
- [12] R. Temam, Une méthode d’approximation de la solution des équations de Navier-Stokes. Bull. Soc. Math. France 98 (1968) 115-152. Zbl0181.18903
- [13] B.A. Ton, Optimal shape control problems for the Navier-Stokes equations. SIAM J. Control Optim. 41 (2003) 1733-1747. Zbl1037.49035MR1972531