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Volumn 53, Issue 4, 2007, Pages 573-597

On stabilized finite element methods for the Stokes problem in the small time step limit

Author keywords

Inf sup; Small time step limit; Stabilized finite element methods; SVD; Unsteady Stokes equations

Indexed keywords

APPROXIMATION THEORY; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; NAVIER STOKES EQUATIONS; UNSTEADY FLOW;

EID: 33846412953     PISSN: 02712091     EISSN: 10970363     Source Type: Journal    
DOI: 10.1002/fld.1295     Document Type: Article
Times cited : (55)

References (43)
  • 5
    • 21244478312 scopus 로고    scopus 로고
    • An absolutely stable pressure-Poisson stabilized method for the Stokes equations
    • Bochev P, Gunzburger M. An absolutely stable pressure-Poisson stabilized method for the Stokes equations. SIAM Journal on Numerical Analysis 2005; 42(3):1189-1207.
    • (2005) SIAM Journal on Numerical Analysis , vol.42 , Issue.3 , pp. 1189-1207
    • Bochev, P.1    Gunzburger, M.2
  • 6
    • 0000698561 scopus 로고
    • Stabilized mixed methods for the Stokes problem
    • Brezzi F, Douglas J. Stabilized mixed methods for the Stokes problem. Numerische Mathematik 1988; 53:225-235.
    • (1988) Numerische Mathematik , vol.53 , pp. 225-235
    • Brezzi, F.1    Douglas, J.2
  • 7
    • 84966220003 scopus 로고
    • An absolutely stabilized finite element method for the Stokes problem
    • Douglas J, Wang J. An absolutely stabilized finite element method for the Stokes problem. Mathematics of Computation 1989; 52:495-508.
    • (1989) Mathematics of Computation , vol.52 , pp. 495-508
    • Douglas, J.1    Wang, J.2
  • 8
    • 0002212220 scopus 로고
    • Stabilized finite element methods
    • In Gunzburger M, Nicolaides R (eds). Cambridge University Press: Cambridge, MA
    • Franca L, Hughes TJR, Stenberg R. Stabilized finite element methods. In Incompressible Computational Fluid Dynamics, Gunzburger M, Nicolaides R (eds). Cambridge University Press: Cambridge, MA, 1993; 87-108.
    • (1993) Incompressible Computational Fluid Dynamics , pp. 87-108
    • Franca, L.1    Hughes, T.J.R.2    Stenberg, R.3
  • 9
    • 45149144830 scopus 로고
    • A new finite element formulation for computational fluid dynamics: VIII. The Galerkin/least-squares method for advective-diffusive equations
    • Hughes TJR, Franca LP, Hulbert G. A new finite element formulation for computational fluid dynamics: VIII. The Galerkin/least-squares method for advective-diffusive equations. Computer Methods in Applied Mechanics and Engineering 1989; 73:173-189.
    • (1989) Computer Methods in Applied Mechanics and Engineering , vol.73 , pp. 173-189
    • Hughes, T.J.R.1    Franca, L.P.2    Hulbert, G.3
  • 10
    • 0023450642 scopus 로고
    • A new finite element formulation for computational fluid dynamics: VII. The Stokes problem with various well-posed boundary conditions: Symmetric formulations that converge for all velocity pressure spaces
    • Hughes TJR, Franca L. A new finite element formulation for computational fluid dynamics: VII. The Stokes problem with various well-posed boundary conditions: symmetric formulations that converge for all velocity pressure spaces. Computer Methods in Applied Mechanics and Engineering 1987; 65:85-96.
    • (1987) Computer Methods in Applied Mechanics and Engineering , vol.65 , pp. 85-96
    • Hughes, T.J.R.1    Franca, L.2
  • 11
    • 0022810283 scopus 로고
    • A new finite element formulation for computational fluid dynamics: Circumventing the Babuska-Brezzi condition: A stable Petrov-Galerkin formulation of the Stokes problem accommodating equal-order interpolations
    • Hughes TJR, Franca L, Balestra M. A new finite element formulation for computational fluid dynamics: circumventing the Babuska-Brezzi condition: a stable Petrov-Galerkin formulation of the Stokes problem accommodating equal-order interpolations. Computer Methods in Applied Mechanics and Engineering 1986; 59:85-99.
    • (1986) Computer Methods in Applied Mechanics and Engineering , vol.59 , pp. 85-99
    • Hughes, T.J.R.1    Franca, L.2    Balestra, M.3
  • 13
    • 33646374284 scopus 로고    scopus 로고
    • Finite elements and fast iterative solvers with applications in incompressible fluid dynamics
    • Oxford University Press: Oxford
    • Elman HC, Silvester DJ, Wathen AJ. Finite elements and fast iterative solvers with applications in incompressible fluid dynamics. Numerical Mathematics and Scientific Computation. Oxford University Press: Oxford, 2005.
    • (2005) Numerical Mathematics and Scientific Computation
    • Elman, H.C.1    Silvester, D.J.2    Wathen, A.J.3
  • 14
    • 0026928030 scopus 로고
    • Stabilized finite element methods: II. The incompressible Navier-Stokes equations
    • Franca LP, Frey S. Stabilized finite element methods: II. The incompressible Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering 1991; 99:209-233.
    • (1991) Computer Methods in Applied Mechanics and Engineering , vol.99 , pp. 209-233
    • Franca, L.P.1    Frey, S.2
  • 15
    • 0019607241 scopus 로고
    • Streamline upwind/Petrov-Galerkin formulation for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
    • Hughes TJR, Brooks A. Streamline upwind/Petrov-Galerkin formulation for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering 1982; 32:199-259.
    • (1982) Computer Methods in Applied Mechanics and Engineering , vol.32 , pp. 199-259
    • Hughes, T.J.R.1    Brooks, A.2
  • 16
    • 0020259662 scopus 로고
    • A theoretical framework for Petrov-Galerkin methods with discontinuous weighting functions: Application to the streamline-upwind procedure
    • In Gallagher RH et al. (eds). Wiley
    • Hughes TJR, Brooks A. A theoretical framework for Petrov-Galerkin methods with discontinuous weighting functions: application to the streamline-upwind procedure. In Finite Elements in Fluids, Gallagher RH et al. (eds). vol. 4. Wiley, 1982; 47-65.
    • (1982) Finite Elements in Fluids , vol.4 , pp. 47-65
    • Hughes, T.J.R.1    Brooks, A.2
  • 20
    • 0034351657 scopus 로고    scopus 로고
    • On an improved unusual stabilized finite element method for the advective-reactive-diffusive equation
    • Franca LP, Valentin F. On an improved unusual stabilized finite element method for the advective-reactive-diffusive equation. Computer Methods in Applied Mechanics and Engineering 2000; 190:1785-1800.
    • (2000) Computer Methods in Applied Mechanics and Engineering , vol.190 , pp. 1785-1800
    • Franca, L.P.1    Valentin, F.2
  • 23
    • 33745965783 scopus 로고    scopus 로고
    • Fourier analysis of semi-discrete and space-time stabilized methods for the advective-diffusive-reactive equation: III. SGS/GSGS
    • in press
    • Hauke G, Doweidar MH. Fourier analysis of semi-discrete and space-time stabilized methods for the advective-diffusive-reactive equation: III. SGS/GSGS. Computer Methods in Applied Mechanics and Engineering, in press.
    • Computer Methods in Applied Mechanics and Engineering
    • Hauke, G.1    Doweidar, M.H.2
  • 24
    • 2042455855 scopus 로고    scopus 로고
    • Stability of semidiscrete formulations for parabolic problems at small time steps
    • Harari I. Stability of semidiscrete formulations for parabolic problems at small time steps. Computer Methods in Applied Mechanics and Engineering 2004; 193(15-16):1491-1516.
    • (2004) Computer Methods in Applied Mechanics and Engineering , vol.193 , Issue.15-16 , pp. 1491-1516
    • Harari, I.1
  • 26
    • 0036906639 scopus 로고    scopus 로고
    • The finite element method for elliptic problems
    • SIAM: Philadelphia
    • Ciarlet P. The finite element method for elliptic problems. SIAM Classics in Applied Mathematics SIAM: Philadelphia, 2002.
    • (2002) SIAM Classics in Applied Mathematics
    • Ciarlet, P.1
  • 27
    • 0000522620 scopus 로고
    • On existence, uniqueness and approximation of saddle-point problems arising from Lagrange multipliers
    • Brezzi F. On existence, uniqueness and approximation of saddle-point problems arising from Lagrange multipliers. Mathematical Modeling and Numerical Analysis 1974; 21:129-151.
    • (1974) Mathematical Modeling and Numerical Analysis , vol.21 , pp. 129-151
    • Brezzi, F.1
  • 28
    • 33646371000 scopus 로고    scopus 로고
    • Regularization and stabilization of discrete saddle-point variational problems
    • Bochev P, Lehoucq R. Regularization and stabilization of discrete saddle-point variational problems. Electronic Transactions on Numerical Analysis 2006; 22:97-113.
    • (2006) Electronic Transactions on Numerical Analysis , vol.22 , pp. 97-113
    • Bochev, P.1    Lehoucq, R.2
  • 29
    • 20044365185 scopus 로고    scopus 로고
    • Stability of saddle-points in finite dimensions
    • In Blowey J, Craig A, Shardlow T (eds). Springer: Berlin
    • Brezzi F. Stability of saddle-points in finite dimensions. In Frontiers in Numerical Analysis, Blowey J, Craig A, Shardlow T (eds). Springer: Berlin, 2002; 17-61.
    • (2002) Frontiers in Numerical Analysis , pp. 17-61
    • Brezzi, F.1
  • 31
    • 0026155973 scopus 로고
    • A new finite element formulation for computational fluid dynamics: IX. Fourier analysis of space-time Galerkin/least-squares algorithms
    • Shakib F, Hughes TJR. A new finite element formulation for computational fluid dynamics: IX. Fourier analysis of space-time Galerkin/ least-squares algorithms. Computer Methods in Applied Mechanics and Engineering 1991; 87:35-58.
    • (1991) Computer Methods in Applied Mechanics and Engineering , vol.87 , pp. 35-58
    • Shakib, F.1    Hughes, T.J.R.2
  • 32
    • 0026206734 scopus 로고
    • A new finite element formulation for computational fluid dynamics: X. The compressible Euler and Navier-Stokes equations
    • Shakib F, Hughes TJR, Johan Z. A new finite element formulation for computational fluid dynamics: X. The compressible Euler and Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering 1991; 89:141-219.
    • (1991) Computer Methods in Applied Mechanics and Engineering , vol.89 , pp. 141-219
    • Shakib, F.1    Hughes, T.J.R.2    Johan, Z.3
  • 33
    • 17444403192 scopus 로고    scopus 로고
    • On the finite element solution of the pure Neumann problem
    • Bochev P, Lehoucq R. On the finite element solution of the pure Neumann problem. SIAM Review 2005; 47:50-66.
    • (2005) SIAM Review , vol.47 , pp. 50-66
    • Bochev, P.1    Lehoucq, R.2
  • 34
    • 0003130485 scopus 로고
    • On the stabilization of finite element approximations of the Stokes problem
    • In Hackbusch W (ed.). Notes on Numerical Fluid Mechanics, Braunschweig: Wiesbaden, Viewig
    • Brezzi F, Pitkaranta J. On the stabilization of finite element approximations of the Stokes problem. In Efficient Solutions of Elliptic Systems, Hackbusch W (ed.). Notes on Numerical Fluid Mechanics, vol. 10. Braunschweig: Wiesbaden, Viewig, 1984; 11-19.
    • (1984) Efficient Solutions of Elliptic Systems , vol.10 , pp. 11-19
    • Brezzi, F.1    Pitkaranta, J.2
  • 35
    • 0004236492 scopus 로고    scopus 로고
    • (3rd edn). Johns Hopkins University Press: Baltimore, MD
    • Golub G, Van Loan C. Matrix Computations (3rd edn). Johns Hopkins University Press: Baltimore, MD, 1996.
    • (1996) Matrix Computations
    • Golub, G.1    Van Loan, C.2
  • 38
    • 4344609992 scopus 로고    scopus 로고
    • A stabilized finite element method for the Stokes problem based on polynomial pressure projections
    • Dohrmann C, Bochev P. A stabilized finite element method for the Stokes problem based on polynomial pressure projections. International Journal for Numerical Methods in Fluids 2004; 46:183-201.
    • (2004) International Journal for Numerical Methods in Fluids , vol.46 , pp. 183-201
    • Dohrmann, C.1    Bochev, P.2
  • 39
    • 33751528291 scopus 로고    scopus 로고
    • Stabilization of low-order mixed finite elements for the Stokes equations
    • Bochev P, Dohrmann C, Gunzburger MD. Stabilization of low-order mixed finite elements for the Stokes equations. SIAM Journal on Numerical Analysis 2006; 44(1):82-101.
    • (2006) SIAM Journal on Numerical Analysis , vol.44 , Issue.1 , pp. 82-101
    • Bochev, P.1    Dohrmann, C.2    Gunzburger, M.D.3
  • 40
    • 0025404289 scopus 로고
    • Stabilized bilinear-constant velocity-pressure finite elements for the conjugate gradient solution of the Stokes problem
    • Silvester DJ, Kechkar N. Stabilized bilinear-constant velocity-pressure finite elements for the conjugate gradient solution of the Stokes problem. Computer Methods in Applied Mechanics and Engineering 1990; 79:71-86.
    • (1990) Computer Methods in Applied Mechanics and Engineering , vol.79 , pp. 71-86
    • Silvester, D.J.1    Kechkar, N.2
  • 43
    • 0033204955 scopus 로고    scopus 로고
    • Towards discrete Velte decompositions and narrow bounds for inf-sup, constants
    • Stoyan G. Towards discrete Velte decompositions and narrow bounds for inf-sup, constants. Computers and Mathematics with Applications 1999; 38:243-261.
    • (1999) Computers and Mathematics With Applications , vol.38 , pp. 243-261
    • Stoyan, G.1


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