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Volumn 195, Issue 13-16, 2006, Pages 1692-1708

Quadratic finite elements and incompressible viscous flows

Author keywords

Finite element; Incompressible flow; Iterative solver; Pressure stabilization; Schur complement

Indexed keywords

APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; FINITE ELEMENT METHOD; GALERKIN METHODS; ITERATIVE METHODS; NAVIER STOKES EQUATIONS; POLYNOMIALS; VISCOUS FLOW;

EID: 30944462431     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2005.05.046     Document Type: Article
Times cited : (8)

References (50)
  • 1
    • 34250459417 scopus 로고
    • The finite element method with Lagrangian multipliers
    • I. Babuska The finite element method with Lagrangian multipliers Numer. Math. 20 1973 179-192
    • (1973) Numer. Math. , vol.20 , pp. 179-192
    • Babuska, I.1
  • 2
    • 0016093926 scopus 로고
    • On the existence, uniqueness and approximation of saddle-point problems arising from Lagrange multipliers
    • F. Brezzi On the existence, uniqueness and approximation of saddle-point problems arising from Lagrange multipliers RAIRO Ser. Rouge 8 1974 129-151
    • (1974) RAIRO Ser. Rouge , vol.8 , pp. 129-151
    • Brezzi, F.1
  • 4
    • 0019607241 scopus 로고
    • Streamline upwind/Petrov-Galerkin formulations for convective dominated flows with particular emphasis on the incompressible Navier-Stokes equations
    • A.N. Brooks T.J.R. Hughes Streamline upwind/Petrov-Galerkin formulations for convective 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
  • 5
    • 77956849889 scopus 로고
    • Stabilized finite element formulations for incompressible flow computations
    • T.E. Tezduyar Stabilized finite element formulations for incompressible flow computations Adv. Appl. Mech. 28 1992 1-44
    • (1992) Adv. Appl. Mech. , vol.28 , pp. 1-44
    • Tezduyar, T.E.1
  • 6
    • 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
    • T.J.R. Hughes L.P. Franca M. Balestra 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
  • 7
    • 45149144830 scopus 로고
    • A new finite element formulation for computational fluid dynamics: VII. The Galerkin-least squares method for advective-diffusive equations
    • T.J.R. Hughes L.P. Franca G.M. Hulbert A new finite element formulation for computational fluid dynamics: VII. The Galerkin-least squares method for advective-diffusive equations Comput. Methods Appl. Mech. Engrg. 73 1989 173-189
    • (1989) Comput. Methods Appl. Mech. Engrg. , vol.73 , pp. 173-189
    • Hughes, T.J.R.1    Franca, L.P.2    Hulbert, G.M.3
  • 8
    • 0029405472 scopus 로고
    • Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid-scale models, bubbles and the origin of stabilized methods
    • T.J.R. Hughes 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 1387-1401
    • (1995) Comput. Methods Appl. Mech. Engrg. , vol.127 , pp. 1387-1401
    • Hughes, T.J.R.1
  • 10
    • 4344609992 scopus 로고    scopus 로고
    • A stabilized finite element method for the Stokes problem based on polynomial pressure projections
    • C.R. Dohrmann P.B. Bochev A stabilized finite element method for the Stokes problem based on polynomial pressure projections Int. J. Numer. Methods Fluids 46 2004 183-201
    • (2004) Int. J. Numer. Methods Fluids , vol.46 , pp. 183-201
    • Dohrmann, C.R.1    Bochev, P.B.2
  • 11
    • 33751528291 scopus 로고    scopus 로고
    • Stabilization of low-order mixed finite elements for the Stokes equations
    • accepted for publication
    • P.B. Bochev, C.R. Dohrmann, M.D. Gunzburger, Stabilization of low-order mixed finite elements for the Stokes equations, SIAM J. Numer. Anal., accepted for publication.
    • SIAM J. Numer. Anal.
    • Bochev, P.B.1    Dohrmann, C.R.2    Gunzburger, M.D.3
  • 13
    • 0242338413 scopus 로고    scopus 로고
    • Computation of moving boundaries and interfaces and stabilization parameters
    • T.E. Tezduyar Computation of moving boundaries and interfaces and stabilization parameters Int. J. Numer. Methods Fluids 43 2003 555-575
    • (2003) Int. J. Numer. Methods Fluids , vol.43 , pp. 555-575
    • Tezduyar, T.E.1
  • 14
    • 0026928030 scopus 로고
    • Stabilized finite element methods: II. The incompressible Navier-Stokes equations
    • L.P. Franca S.L. Frey 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
  • 15
    • 0026872324 scopus 로고
    • What are C and h? Inequalities for the analysis and design of finite element methods
    • I. Harari T.J.R. Hughes What are C and h? Inequalities for the analysis and design of finite element methods Comput. Methods Appl. Mech. Engrg. 97 1992 157-192
    • (1992) Comput. Methods Appl. Mech. Engrg. , vol.97 , pp. 157-192
    • Harari, I.1    Hughes, T.J.R.2
  • 16
    • 0005988611 scopus 로고    scopus 로고
    • KACHINA - A finite element computer program for viscous, incompressible flow problems
    • Sandia Report, Sandia National Laboratories, Albuquerque, NM, in preparation
    • D.K. Gartling, KACHINA - a finite element computer program for viscous, incompressible flow problems, Sandia Report, Sandia National Laboratories, Albuquerque, NM, in preparation.
    • Gartling, D.K.1
  • 17
    • 0034287411 scopus 로고    scopus 로고
    • Finite element stabilization parameters computed from element matrics and vectors
    • T.E. Tezduyar Y. Osawa Finite element stabilization parameters computed from element matrics and vectors Comput. Methods Appl. Mech. Engrg. 190 2000 411-430
    • (2000) Comput. Methods Appl. Mech. Engrg. , vol.190 , pp. 411-430
    • Tezduyar, T.E.1    Osawa, Y.2
  • 18
    • 0000048673 scopus 로고
    • GMRES: A generalized minimum residual algorithm for solving nonsymmetric linear systems
    • Y. Saad M.H. Schultz GMRES: A generalized minimum residual algorithm for solving nonsymmetric linear systems SIAM J. Sci. Statist. Comput. 7 1986 856-869
    • (1986) SIAM J. Sci. Statist. Comput. , vol.7 , pp. 856-869
    • Saad, Y.1    Schultz, M.H.2
  • 20
    • 30944436077 scopus 로고    scopus 로고
    • A study of two domain decomposition preconditioners
    • Sandia Report, SAND2003-4391, Sandia National Laboratories, Albuquerque, NM
    • C.R. Dohrmann, A study of two domain decomposition preconditioners, Sandia Report, SAND2003-4391, Sandia National Laboratories, Albuquerque, NM, 2003.
    • (2003)
    • Dohrmann, C.R.1
  • 21
    • 1842564155 scopus 로고    scopus 로고
    • A preconditioner for substructuring based on constrained energy minimization
    • C.R. Dohrmann A preconditioner for substructuring based on constrained energy minimization SIAM J. Sci. Comput. 25 2003 246-258
    • (2003) SIAM J. Sci. Comput. , vol.25 , pp. 246-258
    • Dohrmann, C.R.1
  • 22
    • 0242287760 scopus 로고    scopus 로고
    • Convergence of a balancing domain decomposition by constraints and energy minimization
    • J. Mandel C.R. Dohrmann Convergence of a balancing domain decomposition by constraints and energy minimization Numer. Linear Algebra Appl. 10 2003 639-659
    • (2003) Numer. Linear Algebra Appl. , vol.10 , pp. 639-659
    • Mandel, J.1    Dohrmann, C.R.2
  • 23
    • 0040997235 scopus 로고
    • Preconditioning of indefinite problems by regularization
    • O. Axelsson Preconditioning of indefinite problems by regularization SIAM J. Numer. Anal. 16 1979 58-69
    • (1979) SIAM J. Numer. Anal. , vol.16 , pp. 58-69
    • Axelsson, O.1
  • 24
    • 21144466078 scopus 로고
    • Multilevel iterative methods for mixed finite element discretizations of elliptic problems
    • P.S. Vassilevski J. Wang Multilevel iterative methods for mixed finite element discretizations of elliptic problems Numer. Math. 63 1992 503-520
    • (1992) Numer. Math. , vol.63 , pp. 503-520
    • Vassilevski, P.S.1    Wang, J.2
  • 25
    • 0040124266 scopus 로고
    • Multilevel iteration for mixed finite element systems with penalty
    • Z. Cai C.I. Goldstein J.E. Pasciak Multilevel iteration for mixed finite element systems with penalty SIAM J. Sci. Comput. 14 1993 1072-1088
    • (1993) SIAM J. Sci. Comput. , vol.14 , pp. 1072-1088
    • Cai, Z.1    Goldstein, C.I.2    Pasciak, J.E.3
  • 26
    • 0642306100 scopus 로고    scopus 로고
    • A note on optimal hybrid V-cycle multilevel algorithms for mixed finite elements systems with penalty term
    • C.G. Lai A note on optimal hybrid V-cycle multilevel algorithms for mixed finite elements systems with penalty term Numer. Linear Algebra Appl. 4 1997 491-498
    • (1997) Numer. Linear Algebra Appl. , vol.4 , pp. 491-498
    • Lai, C.G.1
  • 27
    • 0024663789 scopus 로고
    • Some iterative methods for incompressible flow problems
    • M. Fortin Some iterative methods for incompressible flow problems Comput. Phys. Commun. 53 1989 393-399
    • (1989) Comput. Phys. Commun. , vol.53 , pp. 393-399
    • Fortin, M.1
  • 28
    • 0028517184 scopus 로고
    • Fast iterative solution of stabilised stokes systems. Part II: Using general block preconditioners
    • D. Silvester A. Wathen Fast iterative solution of stabilised stokes systems. Part II: Using general block preconditioners SIAM J. Numer. Anal. 31 1994 1352-1367
    • (1994) SIAM J. Numer. Anal. , vol.31 , pp. 1352-1367
    • Silvester, D.1    Wathen, A.2
  • 29
    • 0002160502 scopus 로고    scopus 로고
    • Fast nonsymmetric iterations and preconditioning for Navier-Stokes equations
    • H. Elman D. Silvester Fast nonsymmetric iterations and preconditioning for Navier-Stokes equations SIAM J. Sci. Comput. 17 1996 33-46
    • (1996) SIAM J. Sci. Comput. , vol.17 , pp. 33-46
    • Elman, H.1    Silvester, D.2
  • 30
    • 11744343493 scopus 로고    scopus 로고
    • An optimal preconditioner for a class of saddle point problems with a penalty term
    • A. Klawonn An optimal preconditioner for a class of saddle point problems with a penalty term SIAM J. Sci. Comput. 19 1998 540-552
    • (1998) SIAM J. Sci. Comput. , vol.19 , pp. 540-552
    • Klawonn, A.1
  • 31
    • 11744250187 scopus 로고    scopus 로고
    • Block-triangular preconditioners for saddle point problems with a penalty term
    • A. Klawonn Block-triangular preconditioners for saddle point problems with a penalty term SIAM J. Sci. Comput. 19 1998 172-184
    • (1998) SIAM J. Sci. Comput. , vol.19 , pp. 172-184
    • Klawonn, A.1
  • 32
    • 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 A.J. Wathen Performance and analysis of saddle point preconditioners for the discrete steady-state Navier-Stokes equations Numer. Math. 90 2002 665-688
    • (2002) Numer. Math. , vol.90 , pp. 665-688
    • Elman, H.C.1    Silvester, D.J.2    Wathen, A.J.3
  • 33
    • 0037250656 scopus 로고    scopus 로고
    • A preconditioner for the steady-state Navier-Stokes equations
    • D. Kay D. Loghin A. Wathen A preconditioner for the steady-state Navier-Stokes equations SIAM J. Sci. Comput. 24 2002 237-256
    • (2002) SIAM J. Sci. Comput. , vol.24 , pp. 237-256
    • Kay, D.1    Loghin, D.2    Wathen, A.3
  • 34
    • 0038286336 scopus 로고    scopus 로고
    • A parallel block multi-level preconditioner for the 3D incompressible Navier-Stokes equations
    • H.C. Elman V.E. Howle J.N. Shadid R.S. Tuminaro A parallel block multi-level preconditioner for the 3D incompressible Navier-Stokes equations J. Comput. Phys. 187 2003 504-523
    • (2003) J. Comput. Phys. , vol.187 , pp. 504-523
    • Elman, H.C.1    Howle, V.E.2    Shadid, J.N.3    Tuminaro, R.S.4
  • 35
    • 0028741633 scopus 로고
    • Inexact and preconditioned Uzawa algorithms for saddle point problems
    • H.C. Elman G.H. Golub Inexact and preconditioned Uzawa algorithms for saddle point problems SIAM J. Numer. Anal. 31 1994 1645-1661
    • (1994) SIAM J. Numer. Anal. , vol.31 , pp. 1645-1661
    • Elman, H.C.1    Golub, G.H.2
  • 36
    • 0001341650 scopus 로고    scopus 로고
    • Analysis of the inexact Uzawa algorithm for saddle point problems
    • J.H. Bramble J.E. Pasciak A.T. Vassilev Analysis of the inexact Uzawa algorithm for saddle point problems SIAM J. Numer. Anal. 34 1997 1072-1092
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 1072-1092
    • Bramble, J.H.1    Pasciak, J.E.2    Vassilev, A.T.3
  • 37
    • 1842788000 scopus 로고    scopus 로고
    • A nested iterative scheme for indefinite linear systems in particulate flows
    • A. Baggag A. Sameh A nested iterative scheme for indefinite linear systems in particulate flows Comput. Methods Appl. Mech. Engrg. 193 2004 1923-1957
    • (2004) Comput. Methods Appl. Mech. Engrg. , vol.193 , pp. 1923-1957
    • Baggag, A.1    Sameh, A.2
  • 38
    • 0032476421 scopus 로고    scopus 로고
    • Overlapping Schwarz methods for mixed linear elasticity and Stokes problems
    • A. Klawonn L.F. Pavarino Overlapping Schwarz methods for mixed linear elasticity and Stokes problems Comput. Methods Appl. Mech. Engrg. 165 1998 233-245
    • (1998) Comput. Methods Appl. Mech. Engrg. , vol.165 , pp. 233-245
    • Klawonn, A.1    Pavarino, L.F.2
  • 39
    • 0033923331 scopus 로고    scopus 로고
    • Indefinite overlapping Schwarz methods for time-dependent Stokes problems
    • L.F. Pavarino Indefinite overlapping Schwarz methods for time-dependent Stokes problems Comput. Methods Appl. Mech. Engrg. 187 2000 35-51
    • (2000) Comput. Methods Appl. Mech. Engrg. , vol.187 , pp. 35-51
    • Pavarino, L.F.1
  • 40
    • 20044365729 scopus 로고    scopus 로고
    • Dual-primal FETI methods for stationary Stokes and Navier-Stokes equations
    • Doctoral dissertation, Department of Computer Science, Courant Institute
    • J. Li, Dual-primal FETI methods for stationary Stokes and Navier-Stokes equations, Doctoral dissertation, Department of Computer Science, Courant Institute, 2002.
    • (2002)
    • Li, J.1
  • 41
    • 0036112010 scopus 로고    scopus 로고
    • Balancing Neumann-Neumann methods for incompressible Stokes equations
    • L.F. Pavarino O.B. Widlund Balancing Neumann-Neumann methods for incompressible Stokes equations Comm. Pure Appl. Math. 55 2002 302-335
    • (2002) Comm. Pure Appl. Math. , vol.55 , pp. 302-335
    • Pavarino, L.F.1    Widlund, O.B.2
  • 42
    • 0041414832 scopus 로고    scopus 로고
    • Balancing Neumann-Neumann preconditioners for mixed approximations of heterogeneous problems in linear elasticity
    • P. Goldfeld L.F. Pavarino O.B. Widlund Balancing Neumann-Neumann preconditioners for mixed approximations of heterogeneous problems in linear elasticity Numer. Math. 95 2003 283-324
    • (2003) Numer. Math. , vol.95 , pp. 283-324
    • Goldfeld, P.1    Pavarino, L.F.2    Widlund, O.B.3
  • 43
    • 0001566269 scopus 로고    scopus 로고
    • Multigrid and Krylov subspace methods for the discrete Stokes equations
    • H.C. Elman Multigrid and Krylov subspace methods for the discrete Stokes equations Int. J. Numer. Methods Fluids 22 1996 755-770
    • (1996) Int. J. Numer. Methods Fluids , vol.22 , pp. 755-770
    • Elman, H.C.1
  • 44
    • 0034380208 scopus 로고    scopus 로고
    • A comparison of overlapping Schwarz methods and block preconditioners for saddle point problems
    • A. Klawonn L.F. Pavarino A comparison of overlapping Schwarz methods and block preconditioners for saddle point problems Numer. Linear Algebra Appl. 7 2000 1-25
    • (2000) Numer. Linear Algebra Appl. , vol.7 , pp. 1-25
    • Klawonn, A.1    Pavarino, L.F.2
  • 45
    • 0000954680 scopus 로고
    • A flexible inner-outer preconditioned GMRES algorithm
    • Y. Saad A flexible inner-outer preconditioned GMRES algorithm SIAM J. Sci. Statist. Comput. 14 1993 461-469
    • (1993) SIAM J. Sci. Statist. Comput. , vol.14 , pp. 461-469
    • Saad, Y.1
  • 46
    • 20044366132 scopus 로고    scopus 로고
    • A primal based penalty preconditioner for elliptic saddle point systems
    • Sandia Report, SAND2004-5964J, Sandia National Laboratories, Albuquerque, NM
    • C.R. Dohrmann, R.B. Lehoucq, A primal based penalty preconditioner for elliptic saddle point systems, Sandia Report, SAND2004-5964J, Sandia National Laboratories, Albuquerque, NM, 2004.
    • (2004)
    • Dohrmann, C.R.1    Lehoucq, R.B.2
  • 48
    • 12844259250 scopus 로고    scopus 로고
    • Department of Computer and Information Science and Engineering, University of Florida, Gainesville, Florida
    • T.A. Davis, UMFPACK Version 4.3 User Guide, Department of Computer and Information Science and Engineering, University of Florida, Gainesville, Florida, 2004.
    • (2004) UMFPACK Version 4.3 User Guide
    • Davis, T.A.1
  • 49
    • 0037249694 scopus 로고    scopus 로고
    • GMRES with deflated restarting
    • R.B. Morgan GMRES with deflated restarting SIAM J. Sci. Comput. 24 2002 20-37
    • (2002) SIAM J. Sci. Comput. , vol.24 , pp. 20-37
    • Morgan, R.B.1
  • 50
    • 30944443976 scopus 로고    scopus 로고
    • Sandia Report, SAND2003-2952 Sandia National Laboratories, Albuquerque, NM
    • M.A. Heroux, J.M. Willenbring, Trilinos Users Guide, Sandia Report, SAND2003-2952 Sandia National Laboratories, Albuquerque, NM, 2003.
    • (2003) Trilinos Users Guide
    • Heroux, M.A.1    Willenbring, J.M.2


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