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Volumn 196, Issue 4-6, 2007, Pages 853-866

Stabilized finite element methods for the generalized Oseen problem

Author keywords

Incompressible flow; Navier Stokes equations; Stabilized finite elements; Variational multiscale methods

Indexed keywords

COMPUTER SIMULATION; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; NAVIER STOKES EQUATIONS; PROBLEM SOLVING;

EID: 33751063874     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2006.07.011     Document Type: Article
Times cited : (175)

References (41)
  • 1
    • 0001167160 scopus 로고    scopus 로고
    • A finite element pressure gradient stabilization for the Stokes equations based on local projections
    • Becker R., and Braack M. A finite element pressure gradient stabilization for the Stokes equations based on local projections. Calcolo 38 4 (2001) 173-199
    • (2001) Calcolo , vol.38 , Issue.4 , pp. 173-199
    • Becker, R.1    Braack, M.2
  • 2
    • 20444439564 scopus 로고    scopus 로고
    • Parameter identification for chemical models in combustion problems
    • Becker R., Braack M., and Vexler B. Parameter identification for chemical models in combustion problems. Appl. Numer. Math. 54 3-4 (2005) 519-536
    • (2005) Appl. Numer. Math. , vol.54 , Issue.3-4 , pp. 519-536
    • Becker, R.1    Braack, M.2    Vexler, B.3
  • 3
    • 33751034242 scopus 로고    scopus 로고
    • Local projection stabilization for the Oseen problem and its interpretation as a variational multiscale method
    • Braack M., and Burman E. Local projection stabilization for the Oseen problem and its interpretation as a variational multiscale method. SIAM J. Numer. Anal. 43 6 (2006) 2544-2566
    • (2006) SIAM J. Numer. Anal. , vol.43 , Issue.6 , pp. 2544-2566
    • Braack, M.1    Burman, E.2
  • 4
    • 33751041009 scopus 로고    scopus 로고
    • F. Brezzi, B. Cockburn, L.D. Marini and E. Süli, Stabilization mechanisms in discontinuous Galerkin finite element methods, Oxford Univ. Comput. Lab., Report no. NA-04/24.
  • 5
    • 0019607241 scopus 로고
    • Streamline upwind Petrov-Galerkin formulation for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
    • Brooks A.N., and Hughes T.J.R. 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
    • (1982) Comput. Methods Appl. Mech. Engrg. , vol.32 , pp. 199-259
    • Brooks, A.N.1    Hughes, T.J.R.2
  • 6
    • 27144504688 scopus 로고    scopus 로고
    • Stabilized Galerkin methods for convection-reaction-diffusion equations: discrete maximum principle and convergence
    • Burman E., and Ern A. Stabilized Galerkin methods for convection-reaction-diffusion equations: discrete maximum principle and convergence. Math. Comp. 74 252 (2005) 1637-1652
    • (2005) Math. Comp. , vol.74 , Issue.252 , pp. 1637-1652
    • Burman, E.1    Ern, A.2
  • 7
    • 33745674971 scopus 로고    scopus 로고
    • A unified analysis for conforming and nonconforming stabilized finite element methods using interior penalty
    • Burman E. A unified analysis for conforming and nonconforming stabilized finite element methods using interior penalty. SIAM J. Numer. Anal. 43 5 (2005) 2012-2033
    • (2005) SIAM J. Numer. Anal. , vol.43 , Issue.5 , pp. 2012-2033
    • Burman, E.1
  • 8
    • 2042428741 scopus 로고    scopus 로고
    • Edge stabilization for Galerkin approximations of convection-diffusion problems
    • Burman E., and Hansbo P. Edge stabilization for Galerkin approximations of convection-diffusion problems. Comput. Methods Appl. Mech. Engrg. 193 (2004) 1437-1453
    • (2004) Comput. Methods Appl. Mech. Engrg. , vol.193 , pp. 1437-1453
    • Burman, E.1    Hansbo, P.2
  • 9
    • 33645071596 scopus 로고    scopus 로고
    • A stabilized non-conforming finite element method for incompressible flow
    • Burman E., and Hansbo P. A stabilized non-conforming finite element method for incompressible flow. Comput. Methods Appl. Mech. Engrg. 195 23/24 (2006) 2881-2899
    • (2006) Comput. Methods Appl. Mech. Engrg. , vol.195 , Issue.23-24 , pp. 2881-2899
    • Burman, E.1    Hansbo, P.2
  • 10
    • 33644586167 scopus 로고    scopus 로고
    • Edge stabilization for the generalized Stokes problem: a continuous interior penalty method
    • Burman E., and Hansbo P. Edge stabilization for the generalized Stokes problem: a continuous interior penalty method. Comput. Methods Appl. Mech. Engrg. 195 (2006) 2393-2410
    • (2006) Comput. Methods Appl. Mech. Engrg. , vol.195 , pp. 2393-2410
    • Burman, E.1    Hansbo, P.2
  • 11
    • 33751055136 scopus 로고    scopus 로고
    • E. Burman, A. Ern, Continuous interior penalty hp-finite element methods for transport operators, Math. Comp. (to appear).
  • 12
    • 33751063232 scopus 로고    scopus 로고
    • Continuous interior penalty method for the Oseen's equations
    • Burman E., Fernández M.A., and Hansbo P. Continuous interior penalty method for the Oseen's equations. SIAM J. Numer. Anal. 44 3 (2006) 1248-1274
    • (2006) SIAM J. Numer. Anal. , vol.44 , Issue.3 , pp. 1248-1274
    • Burman, E.1    Fernández, M.A.2    Hansbo, P.3
  • 13
    • 33751057840 scopus 로고    scopus 로고
    • E. Burman, M. Fernández, Stabilized finite element schemes for incompressible flow using velocity/pressure spaces satisfying the LBB-condition, in: Proceedings of the 6th World Congress in Computational Mechanics, WCCM VI, 2004.
  • 14
    • 1642602854 scopus 로고    scopus 로고
    • The local discontinuous Galerkin method for the Oseen equations
    • Cockburn B., Kanschat G., and Schötzau D. The local discontinuous Galerkin method for the Oseen equations. Math. Comp. 73 (2004) 569-583
    • (2004) Math. Comp. , vol.73 , pp. 569-583
    • Cockburn, B.1    Kanschat, G.2    Schötzau, D.3
  • 15
    • 0031122288 scopus 로고    scopus 로고
    • A finite element formulation of the Stokes problem allowing equal velocity-pressure interpolation
    • Codina R., and Blasco J. A finite element formulation of the Stokes problem allowing equal velocity-pressure interpolation. Comput. Methods Appl. Mech. Engrg. 143 (1997) 373-391
    • (1997) Comput. Methods Appl. Mech. Engrg. , vol.143 , pp. 373-391
    • Codina, R.1    Blasco, J.2
  • 16
    • 0034351658 scopus 로고    scopus 로고
    • Stabilization of incompressibility and convection through orthogonal subscales in finite element methods
    • Codina R. Stabilization of incompressibility and convection through orthogonal subscales in finite element methods. Comput. Methods Appl. Mech. Engrg. 190 13/14 (2000) 1579-1599
    • (2000) Comput. Methods Appl. Mech. Engrg. , vol.190 , Issue.13-14 , pp. 1579-1599
    • Codina, R.1
  • 17
    • 0001456343 scopus 로고
    • Interior penalty procedures for elliptic and parabolic Galerkin methods
    • Computing Methods in Applied Sciences (Second International Symposium, Versailles, 1975), Springer, Berlin
    • Douglas J., and Dupont T. Interior penalty procedures for elliptic and parabolic Galerkin methods. Computing Methods in Applied Sciences (Second International Symposium, Versailles, 1975). Lecture Notes in Physics vol. 58 (1976), Springer, Berlin 207-216
    • (1976) Lecture Notes in Physics , vol.58 , pp. 207-216
    • Douglas, J.1    Dupont, T.2
  • 18
    • 0026928030 scopus 로고
    • Stabilized finite element methods: II. The incompressible Navier-Stokes equations
    • Franca L.P., and Frey S.L. Stabilized finite element methods: II. The incompressible Navier-Stokes equations. Comput. Methods Appl. Mech. Engrg. 99 (1992) 209-233
    • (1992) Comput. Methods Appl. Mech. Engrg. , vol.99 , pp. 209-233
    • Franca, L.P.1    Frey, S.L.2
  • 19
    • 0026386228 scopus 로고
    • Error analysis of some Galerkin-least-squares methods for the elasticity equations
    • Franca L.P., and Stenberg R. Error analysis of some Galerkin-least-squares methods for the elasticity equations. SIAM J. Numer. Anal. 28 (1991) 1680-1697
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 1680-1697
    • Franca, L.P.1    Stenberg, R.2
  • 20
    • 13844275966 scopus 로고    scopus 로고
    • Stabilized finite element schemes with LBB-stable elements for incompressible flows
    • Gelhard T., Lube G., Olshanskii M.O., and Starcke J.H. Stabilized finite element schemes with LBB-stable elements for incompressible flows. J. Comp. Appl. Math. 177 (2005) 243-267
    • (2005) J. Comp. Appl. Math. , vol.177 , pp. 243-267
    • Gelhard, T.1    Lube, G.2    Olshanskii, M.O.3    Starcke, J.H.4
  • 21
    • 11244280117 scopus 로고    scopus 로고
    • A discontinuous Galerkin method with nonoverlapping domain decomposition for the Stokes and Navier-Stokes problems
    • 53-84
    • Girault V., Riviere B., and Wheeler M.F. A discontinuous Galerkin method with nonoverlapping domain decomposition for the Stokes and Navier-Stokes problems. Math. Comp. 74 (2004) 249 53-84
    • (2004) Math. Comp. , vol.74 , pp. 249
    • Girault, V.1    Riviere, B.2    Wheeler, M.F.3
  • 22
    • 0033264647 scopus 로고    scopus 로고
    • Stabilization of Galerkin approximations of transport equations by subgrid modeling
    • Guermond J.-L. Stabilization of Galerkin approximations of transport equations by subgrid modeling. M2AN 33 (1999) 1293-1316
    • (1999) M2AN , vol.33 , pp. 1293-1316
    • Guermond, J.-L.1
  • 23
    • 0025547284 scopus 로고
    • A velocity-pressure streamline diffusion finite element method for the incompressible Navier-Stokes equations
    • Hansbo P., and Szepessy A. A velocity-pressure streamline diffusion finite element method for the incompressible Navier-Stokes equations. Comput. Meths. Appl. Mech. Eng. 84 (1990) 175-192
    • (1990) Comput. Meths. Appl. Mech. Eng. , vol.84 , pp. 175-192
    • Hansbo, P.1    Szepessy, A.2
  • 24
    • 0034963138 scopus 로고    scopus 로고
    • Stabilised hp-finite element approximations of partial differential equations with nonnegative characteristic form
    • Houston P., and Süli E. Stabilised hp-finite element approximations of partial differential equations with nonnegative characteristic form. Computing 66 (2001) 99-119
    • (2001) Computing , vol.66 , pp. 99-119
    • Houston, P.1    Süli, E.2
  • 25
    • 0029405472 scopus 로고
    • Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid-scale models, bubbles and the origin of stabilized methods
    • Hughes T.J.R. Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid-scale models, bubbles and the origin of stabilized methods. Comput. Methods Appl. Mech. Engrg. 127 (1995) 387-401
    • (1995) Comput. Methods Appl. Mech. Engrg. , vol.127 , pp. 387-401
    • Hughes, T.J.R.1
  • 26
    • 0022810283 scopus 로고
    • A new finite element formulation for computational fluid dynamics: V. Circumventing the Babuska-Brezzi condition: a stable Petrov-Galerkin formulation of the Stokes problem accommodating equal-order interpolations
    • Hughes T.J.R., Franca L.P., and Balestra M. A new finite element formulation for computational fluid dynamics: V. Circumventing the Babuska-Brezzi condition: a stable Petrov-Galerkin formulation of the Stokes problem accommodating equal-order interpolations. Comput. Methods Appl. Mech. Engrg. 59 (1986) 85-99
    • (1986) Comput. Methods Appl. Mech. Engrg. , vol.59 , pp. 85-99
    • Hughes, T.J.R.1    Franca, L.P.2    Balestra, M.3
  • 27
    • 0001769879 scopus 로고    scopus 로고
    • Large eddy simulation and the variational multiscale method
    • Hughes T.J., Mazzei L., and Jansen K.E. Large eddy simulation and the variational multiscale method. Comput. Visual. Sci. 3 (2000) 47-59
    • (2000) Comput. Visual. Sci. , vol.3 , pp. 47-59
    • Hughes, T.J.1    Mazzei, L.2    Jansen, K.E.3
  • 28
    • 33751065234 scopus 로고    scopus 로고
    • V. John, S. Kaya, Finite element error analysis of a variational multiscale method for the Navier-Stokes equations. Adv. Comp. Math. (in press).
  • 29
    • 25444505626 scopus 로고    scopus 로고
    • A finite element variational multiscale method for the Navier-Stokes equations
    • John V., and Kaya S. A finite element variational multiscale method for the Navier-Stokes equations. SIAM J. Sci. Comp. 26 (2005) 1485-1503
    • (2005) SIAM J. Sci. Comp. , vol.26 , pp. 1485-1503
    • John, V.1    Kaya, S.2
  • 30
    • 33646487464 scopus 로고    scopus 로고
    • A two-level variational multiscale method for convection-dominated convection-diffusion equations
    • John V., Kaya S., and Layton W. A two-level variational multiscale method for convection-dominated convection-diffusion equations. Comput. Methods Appl. Mech. Engrg. 195 (2006) 4594-4603
    • (2006) Comput. Methods Appl. Mech. Engrg. , vol.195 , pp. 4594-4603
    • John, V.1    Kaya, S.2    Layton, W.3
  • 31
    • 84966256937 scopus 로고
    • Streamline diffusion methods for the incompressible Euler and Navier-Stokes equations
    • 1-18
    • Johnson C., and Saranen J. Streamline diffusion methods for the incompressible Euler and Navier-Stokes equations. Math. Comp. 47 (1986) 175 1-18
    • (1986) Math. Comp. , vol.47 , pp. 175
    • Johnson, C.1    Saranen, J.2
  • 32
    • 33751038364 scopus 로고    scopus 로고
    • S. Kaya, W.J. Layton, Subgrid-scale eddy viscosity models are variational multiscale methods, Technical Report TR-MATH 03-05, University of Pittsburgh, 2003.
  • 33
    • 30344470638 scopus 로고    scopus 로고
    • A discontinuous subgrid eddy viscosity method for the time dependent Navier-Stokes equations
    • 157-159
    • Kaya S., and Riviere B. A discontinuous subgrid eddy viscosity method for the time dependent Navier-Stokes equations. SIAM J. Numer. Anal. 43 (2005) 4 157-159
    • (2005) SIAM J. Numer. Anal. , vol.43 , pp. 4
    • Kaya, S.1    Riviere, B.2
  • 34
    • 0037175406 scopus 로고    scopus 로고
    • A connection between subgrid scale eddy viscosity and mixed methods
    • Layton W.J. A connection between subgrid scale eddy viscosity and mixed methods. Appl. Math. Comput. 133 (2002) 147-157
    • (2002) Appl. Math. Comput. , vol.133 , pp. 147-157
    • Layton, W.J.1
  • 35
    • 33751067867 scopus 로고    scopus 로고
    • D. Loghin, Analysis of preconditioned Picard iterations for the Navier-Stokes equations, Report no. 01/10, Oxford University Computing Laboratory, 2001.
  • 36
    • 33746074781 scopus 로고    scopus 로고
    • Residual-based higher-order FEM for a generalized Oseen problem
    • Lube G., and Rapin G. Residual-based higher-order FEM for a generalized Oseen problem. Math. Model. Meth. Appl. Sci. 16 7 (2006) 949-966
    • (2006) Math. Model. Meth. Appl. Sci. , vol.16 , Issue.7 , pp. 949-966
    • Lube, G.1    Rapin, G.2
  • 37
    • 84951671794 scopus 로고
    • Über ein Variationsprinzip zur Lösung von Dirichlet-problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind
    • Nitsche J. Über ein Variationsprinzip zur Lösung von Dirichlet-problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. Abh. Math. Sem. Univ. Hamburg 36 (1971) 9-15
    • (1971) Abh. Math. Sem. Univ. Hamburg , vol.36 , pp. 9-15
    • Nitsche, J.1
  • 38
    • 33751053676 scopus 로고    scopus 로고
    • N. Parolini, E. Burman. Subgrid edge stabilization for transport equations, EPFL/IACS Preprint 09.2005.
  • 39
    • 0001957739 scopus 로고
    • General circulation experiments with the primitive equations
    • Smagorinsky J.S. General circulation experiments with the primitive equations. Mon. Weather Rev. 91 (1963) 99-164
    • (1963) Mon. Weather Rev. , vol.91 , pp. 99-164
    • Smagorinsky, J.S.1
  • 40
    • 0002092907 scopus 로고
    • A modified streamline diffusion method for solving the stationary Navier-Stokes equations
    • Tobiska L., and Lube G. A modified streamline diffusion method for solving the stationary Navier-Stokes equations. Numer. Math. 59 (1991) 13-29
    • (1991) Numer. Math. , vol.59 , pp. 13-29
    • Tobiska, L.1    Lube, G.2
  • 41
    • 0000935072 scopus 로고    scopus 로고
    • Analysis of a streamline-diffusion finite element method for the Stokes and Navier-Stokes equations
    • Tobiska L., and Verfürth R. Analysis of a streamline-diffusion finite element method for the Stokes and Navier-Stokes equations. SIAM Numer. Anal. 33 (1996) 107-127
    • (1996) SIAM Numer. Anal. , vol.33 , pp. 107-127
    • Tobiska, L.1    Verfürth, R.2


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