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Volumn 28, Issue 6, 2006, Pages 2095-2113

An augmented Lagrangian-based approach to the Oseen problem

Author keywords

Finite element; Iterative methods; Multigrid; Navier Stokes equations; Preconditioning

Indexed keywords

ELASTICITY; FINITE ELEMENT METHOD; ITERATIVE METHODS; NAVIER STOKES EQUATIONS; PROBLEM SOLVING; VISCOSITY;

EID: 34548311912     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/050646421     Document Type: Article
Times cited : (232)

References (36)
  • 1
    • 0001619671 scopus 로고
    • Locking effects in the finite element approximation of elasticity problems
    • I. BABUŠKA AND M. SURI, Locking effects in the finite element approximation of elasticity problems, Numer. Math., 62 (1992), pp. 439-463.
    • (1992) Numer. Math , vol.62 , pp. 439-463
    • BABUŠKA, I.1    SURI, M.2
  • 2
    • 20044390432 scopus 로고    scopus 로고
    • Numerical solution of saddle point problems
    • M. BENZI, G. H. GOLUB, AND J. LIESEN, Numerical solution of saddle point problems, Acta Numer., 14 (2005), pp. 1-137.
    • (2005) Acta Numer , vol.14 , pp. 1-137
    • BENZI, M.1    GOLUB, G.H.2    LIESEN, J.3
  • 3
    • 0031074262 scopus 로고    scopus 로고
    • Downwind numbering: Robust multigrid for convection-diffusion problems
    • J. BEY AND G. WITTUM, Downwind numbering: Robust multigrid for convection-diffusion problems, Appl. Numer. Math., 23 (1997), pp. 177-192.
    • (1997) Appl. Numer. Math , vol.23 , pp. 177-192
    • BEY, J.1    WITTUM, G.2
  • 6
    • 0019607241 scopus 로고
    • Streamline upwind/Petrov-Galerkin formulation for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
    • A. N. BROOKS AND T. J. R. HUGHES, 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), pp. 199-259.
    • (1982) Comput. Methods Appl. Mech. Engrg , vol.32 , pp. 199-259
    • BROOKS, A.N.1    HUGHES, T.J.R.2
  • 7
    • 33847652989 scopus 로고    scopus 로고
    • A primal-based penalty preconditioner for elliptic saddle point systems
    • C R. DOHRMANN AND R. B. LEHOUCQ, A primal-based penalty preconditioner for elliptic saddle point systems, SIAM J. Numer. Anal., 44 (2006), pp. 270-282.
    • (2006) SIAM J. Numer. Anal , vol.44 , pp. 270-282
    • DOHRMANN, C.R.1    LEHOUCQ, R.B.2
  • 8
    • 85142206377 scopus 로고    scopus 로고
    • H. ELM AN AND D. SILVESTER, Fast nonsymmetric iterations and preconditioning for the Navier-Stokes equations, SIAM J. Sci. Comput., 17 (1996), pp. 33-46.
    • H. ELM AN AND D. SILVESTER, Fast nonsymmetric iterations and preconditioning for the Navier-Stokes equations, SIAM J. Sci. Comput., 17 (1996), pp. 33-46.
  • 9
    • 0036003235 scopus 로고    scopus 로고
    • Performance and analysis of saddle point preconditioners for the discrete steady-state Navier-Stokes equations
    • H. C. ELMAN, D. J. SILVESTER, AND A. J. WATHEN, Performance and analysis of saddle point preconditioners for the discrete steady-state Navier-Stokes equations, Numer. Math., 90 (2002), pp. 665-688.
    • (2002) Numer. Math , vol.90 , pp. 665-688
    • ELMAN, H.C.1    SILVESTER, D.J.2    WATHEN, A.J.3
  • 11
    • 0033621004 scopus 로고    scopus 로고
    • On parameter choice and iterative convergence for stabilised discretisations of advection-diffusion problems
    • B. FISCHER, A. RAMAGE, D. J. SILVESTER, AND A. J. WATHEN, On parameter choice and iterative convergence for stabilised discretisations of advection-diffusion problems, Comput. Methods Appl. Mech. Engrg., 179 (1999), pp. 179-195.
    • (1999) Comput. Methods Appl. Mech. Engrg , vol.179 , pp. 179-195
    • FISCHER, B.1    RAMAGE, A.2    SILVESTER, D.J.3    WATHEN, A.J.4
  • 14
    • 30944462431 scopus 로고    scopus 로고
    • Quadratic finite elements and incompressible viscous flow
    • D. K. GARTLING AND C R. DOHRMANN, Quadratic finite elements and incompressible viscous flow, Comput. Methods Appl. Mech. Engrg., 195 (2006), pp. 1692-1708.
    • (2006) Comput. Methods Appl. Mech. Engrg , vol.195 , pp. 1692-1708
    • GARTLING, D.K.1    DOHRMANN, C.R.2
  • 15
    • 0347577906 scopus 로고    scopus 로고
    • On solving block-structured indefinite linear systems
    • G. H. GOLUB AND C. GREIF, On solving block-structured indefinite linear systems, SIAM J. Sci. Comput., 24 (2003), pp. 2076-2092.
    • (2003) SIAM J. Sci. Comput , vol.24 , pp. 2076-2092
    • GOLUB, G.H.1    GREIF, C.2
  • 17
    • 84858476393 scopus 로고    scopus 로고
    • Preconditioned for the discretized time-harmonic Maxwell equations in mixed form
    • to appear
    • C. GREIF AND D. SCHÖTZAU, Preconditioned for the discretized time-harmonic Maxwell equations in mixed form, Numer. Linear Algebra Appl., to appear.
    • Numer. Linear Algebra Appl
    • GREIF, C.1    SCHÖTZAU, D.2
  • 18
    • 0031514669 scopus 로고    scopus 로고
    • Downwind Gauss-Seidel smoothing for convection dominated problems
    • W. HACKBUSCH AND T. PROBST, Downwind Gauss-Seidel smoothing for convection dominated problems, Numer. Linear Algebra Appl., 4 (1997), pp. 85-102.
    • (1997) Numer. Linear Algebra Appl , vol.4 , pp. 85-102
    • HACKBUSCH, W.1    PROBST, T.2
  • 19
    • 0037202098 scopus 로고    scopus 로고
    • Higher order finite element methods and multigrid solvers in a benchmark problem for the 3D Navier-Stokes equations
    • V. JOHN, Higher order finite element methods and multigrid solvers in a benchmark problem for the 3D Navier-Stokes equations, Internat. J. Numer. Methods Fluids, 40 (2002), pp. 775-798.
    • (2002) Internat. J. Numer. Methods Fluids , vol.40 , pp. 775-798
    • JOHN, V.1
  • 20
    • 0035977419 scopus 로고    scopus 로고
    • Higher order finite element discretizations in a benchmark problem for incompressible flows
    • V. JOHN AND G. MATTHIES, Higher order finite element discretizations in a benchmark problem for incompressible flows, Internat. J. Numer. Methods Fluids, 37 (2001), pp. 885-903.
    • (2001) Internat. J. Numer. Methods Fluids , vol.37 , pp. 885-903
    • JOHN, V.1    MATTHIES, G.2
  • 21
    • 0037250656 scopus 로고    scopus 로고
    • A preconditioner for the steady-state Navier-Stokes equations
    • D. KAY, D. LOGHIN, AND A. WATHEN, A preconditioner for the steady-state Navier-Stokes equations, SIAM J. Sci. Comput., 24 (2002), pp. 237-256.
    • (2002) SIAM J. Sci. Comput , vol.24 , pp. 237-256
    • KAY, D.1    LOGHIN, D.2    WATHEN, A.3
  • 23
    • 21244493692 scopus 로고    scopus 로고
    • Convergence analysis of a multigrid method for a convection-dominated model problem
    • M. A. OLSHANSKII AND A. REUSKEN, Convergence analysis of a multigrid method for a convection-dominated model problem, SIAM J. Numer. Anal., 42 (2004), pp. 1261-1291.
    • (2004) SIAM J. Numer. Anal , vol.42 , pp. 1261-1291
    • OLSHANSKII, M.A.1    REUSKEN, A.2
  • 24
    • 5644288738 scopus 로고    scopus 로고
    • Grad-div stabilization for Stokes equations
    • M. A. OLSHANSKII AND A. REUSKEN, Grad-div stabilization for Stokes equations, Math. Comp., 73 (2004), pp. 1699-1718.
    • (2004) Math. Comp , vol.73 , pp. 1699-1718
    • OLSHANSKII, M.A.1    REUSKEN, A.2
  • 25
    • 0037159815 scopus 로고    scopus 로고
    • A low order Galerkin finite element method for the Navier-Stokes equations of steady incompressible flow: A stabilization issue and iterative methods
    • M. A. OLSHANSKII, A low order Galerkin finite element method for the Navier-Stokes equations of steady incompressible flow: A stabilization issue and iterative methods, Comput. Methods Appl. Mech. Engrg., 191 (2002), pp. 5515-5536.
    • (2002) Comput. Methods Appl. Mech. Engrg , vol.191 , pp. 5515-5536
    • OLSHANSKII, M.A.1
  • 26
    • 0003208019 scopus 로고
    • Numerical Approximation of Partial Differential Equations
    • Springer, Berlin
    • A. QUARTERONI AND A. VALLI, Numerical Approximation of Partial Differential Equations, Springer Ser. Comput. Math. 23, Springer, Berlin, 1994.
    • (1994) Springer Ser. Comput. Math , vol.23
    • QUARTERONI, A.1    VALLI, A.2
  • 27
    • 0033569547 scopus 로고    scopus 로고
    • A multigrid preconditioner for stabilised discretisations of advection-diffusion problems
    • A. RAMAGE, A multigrid preconditioner for stabilised discretisations of advection-diffusion problems, J. Comput. Appl. Math., 110 (1999), pp. 187-203.
    • (1999) J. Comput. Appl. Math , vol.110 , pp. 187-203
    • RAMAGE, A.1
  • 29
    • 22844455425 scopus 로고    scopus 로고
    • Multigrid methods for a parameter dependent problem in primal variables
    • J. SCHÖBERL, Multigrid methods for a parameter dependent problem in primal variables, Numer. Math., 84 (1999), pp. 97-119.
    • (1999) Numer. Math , vol.84 , pp. 97-119
    • SCHÖBERL, J.1
  • 30
    • 0001845470 scopus 로고
    • BiCGStab(ℓ) for linear equations involving unsymmetric matrices with complex spectrum
    • G. L. G. SLEIJPEN AND D. R. FOKKEMA, BiCGStab(ℓ) for linear equations involving unsymmetric matrices with complex spectrum, Electron. Trans. Numer. Anal., 1 (1993), pp. 11-32.
    • (1993) Electron. Trans. Numer. Anal , vol.1 , pp. 11-32
    • SLEIJPEN, G.L.G.1    FOKKEMA, D.R.2
  • 32
    • 0000005482 scopus 로고
    • Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems
    • H. A. VAN DER VORST, Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems, SIAM J. Sci. Statist. Comput., 13 (1992), pp. 631-644.
    • (1992) SIAM J. Sci. Statist. Comput , vol.13 , pp. 631-644
    • VAN DER VORST, H.A.1
  • 33
    • 46149132843 scopus 로고
    • Block-implicit multigrid solution of Navier-Stokes equations in primitive variables
    • S. P. VANKA, Block-implicit multigrid solution of Navier-Stokes equations in primitive variables, J. Comput. Phys., 65 (1986), pp. 138-158.
    • (1986) J. Comput. Phys , vol.65 , pp. 138-158
    • VANKA, S.P.1
  • 34
    • 0000021772 scopus 로고
    • Realistic eigenvalues bounds for the Galerkin mass matrix
    • A. WATHEN, Realistic eigenvalues bounds for the Galerkin mass matrix, IMA J. Numer. Anal., 7 (1987), pp. 449-457.
    • (1987) IMA J. Numer. Anal , vol.7 , pp. 449-457
    • WATHEN, A.1
  • 35
    • 0035280519 scopus 로고    scopus 로고
    • Geometric multigrid with applications to computational fluid dynamics
    • P. WESSELING AND C. W. OOSTERLEE, Geometric multigrid with applications to computational fluid dynamics, J. Comput. Appl. Math., 128 (2001) pp. 311-334.
    • (2001) J. Comput. Appl. Math , vol.128 , pp. 311-334
    • WESSELING, P.1    OOSTERLEE, C.W.2
  • 36
    • 0000570696 scopus 로고
    • Iterative methods by space decomposition and subspace correction
    • J. XU, Iterative methods by space decomposition and subspace correction, SIAM Rev., 34 (1992), pp. 581-613.
    • (1992) SIAM Rev , vol.34 , pp. 581-613
    • XU, J.1


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