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Sani, R. L.; Gresho, P. M.; Lee, R. L.; Griffiths, D. F.; Engelman, M.

The cause and cure (!) of the spurious pressures generated by certain FEM solutions of the incompressible Navier-Stokes equations. II. (English) Zbl 0461.76022

Int. J. Numer. Methods Fluids 1, 171-204 (1981).
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Cited in 1 Review
Cited in 41 Documents

MSC:

76D05 Navier-Stokes equations for incompressible viscous fluids
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs

Keywords:

spurious pressures; penalty methods; pressure filters

Citations:

Zbl 0461.76021
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Full Text: DOI

References:

[1] Taylor, Computers and Fluids 1 pp 73– (1973)
[2] and , ’Navier-Stokes equations using mixed interpolation’, in Int. Symp on Finite Element Method in Flow Problems, Proceedings, Swansea, Wales (1974).
[3] and , ’Primitive variables versus stream function finite element solutions of the Navier-Stokes equations’, in Finite Elements in Fluids, Volume 3, Wiley, Chichester, 1978, pp. 73-89.
[4] ’Finite elements for incompressible flow’, M.Sc. Dissertation, Dept. Math., University of Reading, UK (1978).
[5] Argyris, Comp. Methods Appl. Mech. and Eng. 4 pp 219– (1974)
[6] Nagtegaal, Comp. Methods Appl. Mech. and Eng. 4 pp 153– (1974)
[7] ’Bilinear finite elements for incompressible flow’, M.Sc. Dissertation, Dept. Math., University of Dundee, Scotland (1977).
[8] Huyakorn, Computers and Fluids 6 pp 25– (1978)
[9] Hughes, J. Comp. Phys. 30 pp 1– (1979)
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[11] ’Numerical solution of steady state Navier-Stokes equations’, in Numerical Methods in Fluid Dynamics (Ed. ), Agard lecture Series No. 48, AGARD-LS-48 (1972).
[12] and , ’BAAL: A code for calculating three-dimensional fluid flows at all speeds with an Eulerian-Lagrangian computing mesh’, Los Alamos Scientific Laboratory Report LA-6342 (1976).
[13] Chorin, Math. of Comp 23 pp 341– (1969)
[14] and , ’On the spurious pressures generated by certain GFEM solutions of the incompressible Navier-Stokes equations’, Third Int. Conf. on Finite Elements in Flow Problems, Proceedings, Banff, Alberta, Canada (1980). · Zbl 0446.76034
[15] Westinghouse Electric Corporation, Pittsburgh, PA, private communication (1979).
[16] Bercovier, J. Comp. Phys. 30 pp 181– (1979)
[17] and , ’On the time-dependent solution of the incompressible Navier-Stokes equations in two and three dimensions’, in Recent Advances in Numerical Methods in Fluids, Pineridge Press, Swansea, U. K., 1980.
[18] Malkus, Comp. Methods Appl. Mech. and Eng. 15 pp 63– (1978)
[19] , and , ’Consistent vs. reduced integration formulations for penalty FEM solutions using several old elements and one new element’, in preparation.
[20] Fortin, RAIRO 11 pp r– (1977)
[21] and , ’Conforming and nonconforming finite element methods for solving the stationary Stokes equations I’, RAIRO Serie Mathematiques, R-3, 33-76 (1973).
[22] and , ’Numerical solition of the stationary Navier-Stokes equations by finite element methods’, Lecture Notes in Computing Sci. Part 1, 193-223, (Ed. and ), Springer-Verlag, 1974.
[23] Brezzi, RAIRO. 8 pp 129– (1974)
[24] ’Finite element methods and Navier-Stokes equations’, in Computing Methods in Applied Science and Engineering, Part 2, (Ed. and ). Lecture Notes 91, Springer-Verlag, New York (1979).
[25] , and , ’A new finite element for Boussinesq fluids’, Third Int. Conf. Finite Elements in Flow Problems, Proceedings, Banff, Alberta, Canada (1980).
[26] ’An approximately divergence-free 9-node velocity element for incompressible flow’, in preparation.
[27] Bercovier, RAIRO Analyse numerique 12 pp 211– (1978)
[28] ’A family of finite elements with penalisation for the numerical solution of Stokes and Navier-Stokes equations’, Information Processing 77, (Ed. ), 97-101, North-Holland (1977).
[29] and , ’Finite element approximations of the Navier-Stokes equations’, Lecture Notes in Math, No. 749, Springer-Verlag (1979).
[30] Reddy, Int. J. Engng Sci. 16 pp 921– (1978)
[31] ’Some remarks on finite element analysis of viscous flow problems’, Third Int. Conf. on Finite Elements in Water Resources, Proceedings, Univ. of Mississippi, Oxford, Miss. (1980).
[32] , and , ’Discrete LBB-conditions for RIP-finite element methods’, TICOM Report 80-7, Texas Institute for Computational Mechanics, University of Texas at Austin (1980).
[33] Personal communication.
[34] Personal communication. (We have since learned, however, that he and Engelman actually achieved filtered pressures, since only centroid values were reported.)
[35] ’Convergence of Penalty/FEM solutions for the Stokes problem’, III. Inst. of Tech. Research Report No. 81-1, for NSF Grant No. CME 80-17549 (1981).
[36] Eyeball method.
[37] ’RIP-methods for Stokesian flows’, TICOM Report 80-11, Texas Institute for Computational Mechanics, University of Texas at Austin (1980).
[38] and , ’Accurate explicit finite element schemes for conductive-Convective heat transfer problems’, in Finite Element Methods for Convection-Dominated Flows, A.S.M.E. publication AMD, Vol. 34 (1979).
[39] Segal, Int. J. num. Meth. Engng 19 pp 165– (1979)
[40] Schneider, Num. Heat Transfer 1 pp 433– (1978)
[41] Bercovier, Numerische Math. 33 pp 211– (1979)
[42] Malkus, J. Eng. Sci.
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