The effect of stabilization in finite element methods for the optimal boundary control of the Oseen equations

Finite Elements in Analysis and Design

Volumn 41, Issue 3, 2004, Pages 229-251

  Abraham, Feby ^a   Behr, Marek ^b   Heinkenschloss, Matthias ^c  

^a Rice University   (United States)

^b TECHNICAL UNIVERSITY OF MUNICH   (Germany)

^c RICE UNIVERSITY   (United States)

Author keywords

Optimal boundary control; Oseen equations; Solution accuracy; Stabilized finite element methods

Indexed keywords

APPROXIMATION THEORY; NAVIER STOKES EQUATIONS; NUMERICAL ANALYSIS; OPTIMAL CONTROL SYSTEMS; PARAMETER ESTIMATION; PARTIAL DIFFERENTIAL EQUATIONS; PROBLEM SOLVING; STABILIZATION;

GALERKIN LEAST-SQUARES (GLS); OPTIMAL BOUNDARY CONTROL; OSEEN EQUATIONS; SOLUTION ACCURACY; STABILIZED FINITE ELEMENT METHODS;

FINITE ELEMENT METHOD;

EID: 12444280088     PISSN: 0168874X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.finel.2004.06.001     Document Type: Article

References (18)

1. A.N. Brooks, and T.J.R. Hughes Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations Comput. Meth. Appl. Mech. Eng. 32 1982 199 259
2. T.J.R. Hughes, L.P. Franca, and M. Balestra A new finite element formulation for computational fluid dynamics: V. Circumventing the Babuška-Brezzi condition a stable Petrov-Galerkin formulation of the Stokes problem accommodating equal-order interpolations Comput. Meth. Appl. Mech. Eng 59 1986 85 99
3. F. Shakib, Finite element analysis of the compressible Euler and Navier-Stokes equations, Ph.D. Thesis, Department of Mechanical Engineering, Stanford University, 1988.
4. L.P. Franca, and S.L. Frey Stabilized finite element methods II. The incompressible Navier-Stokes equations Comput. Meth. Appl. Mech. Eng. 99 1992 209 233
5. T.J.R. Hughes, L.P. Franca, and G.M. Hulbert A new finite element formulation for computational fluid dynamics VIII. The Galerkin/least-squares method for advective-diffusive equations Comput. Meth. Appl. Mech. Eng. 73 1989 173 189
6. M. Heinkenschloss Formulation and analysis of a sequential quadratic programming method for the optimal boundary control of Navier-Stokes flow W.W. Hager P.M. Pardalos Optimal Control: Theory, Algorithms, and Applications 1998 Kluwer Academic Publishers BV. Dordrecht 178 203
7. L.S. Hou, and S.S. Ravindran Numerical approximation of optimal control problems by a penalty method error estimates and numerical results SIAM J. Sci. Comput. 20 1999 1753 1777
8. S.S. Collis, M. Heinkenschloss, Analysis of the streamline-upwind/Petrov- Galerkin method applied to the solution of optimal control problems', Technical Report TR02-01, Department of Computational and Applied Mathematics, Rice University, Houston, TX 77005-1892, 2002, http://www.caam.rice.edu/ ∼ heinken/papers/supg_analysis.html.
9. L.B. Leverett, J.D. Hellums, C.P. Alfrey, and E.C. Lynch Red blood cell damage by shear stress Biophys. J. 12 1972 257 273
10. M.H. Kroll, J.D. Hellums, L.V. McIntire, A.I. Schafer, and J.L. Moake Platelets and shear stress Blood 85 1996 1525 1541
11. R.A. Adams Sobolev Spaces 1975 Academic Press New York
12. O. Ghattas, and J.H. Bark Optimal control of two- and three-dimensional Navier-Stokes flow J. Computat. Phys. 136 1997 231 244
13. M.D. Gunzburger, and L.S. Hou Treating inhomogeneous essential boundary conditions in finite element methods and the calculation of boundary stresses SIAM J. Numerical Anal. 29 1992 390 424
14. L.S. Hou, and S.S. Ravindran A penalized Neumann control approach for solving an optimal Dirichlet control problem for the for the Navier-Stokes equations SIAM J. Control Optim. 36 1998 1795 1814
15. V. Girault, and P.A. Raviart Finite Element Methods for the Navier-Stokes Equations 1986 Springer New York
16. F. Brezzi, and M. Fortin Mixed and hybrid finite element methods, Computational Mathematics, vol. 15 1991 Springer New York
17. T.E. Tezduyar, and Y.J. Park Discontinuity capturing finite element formulations for nonlinear convection-diffusion-reaction problems Comput. Meth. Appl. Mech. Eng. 59 1986 307 325
18. K.E. Jansen, S.S. Collis, C. Whiting, and F. Shakib A better consistency for low-order stabilized finite element methods Comput. Meth. Appl. Mech. Eng. 174 1999 153 170