×

zbMATH — the first resource for mathematics

Finite element analysis of incompressible viscous flows by the penalty function formulation. (English) Zbl 0412.76023

MSC:
76D05 Navier-Stokes equations for incompressible viscous fluids
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
39B99 Functional equations and inequalities
Software:
YAQUI
PDF BibTeX Cite
Full Text: DOI
References:
[1] Amsden, A.A.; Hirt, C.W., YAQUI: an arbitrary Lagrangian-Eulerian computer program for fluid flow at all speeds, Los alamos scientific laboratory, report LA-5100, (March 1973), Los Alamos, New Mexico
[2] Atkinson, J.D.; Hughes, T.J.R., Upwind finite element schemes for convective-diffusive equations, ()
[3] Baker, A.J., A highly stable explicit integration technique for computational continuum mechanics, (), 99-121
[4] Barlow, J., Int. J. num. methods eng., 10, 243-251, (1976)
[5] Batchelor, G.K., An introduction to fluid mechanics, (1970), Cambridge Univ. Press Cambridge, England · Zbl 0152.44402
[6] Bathe, K.J.; Wilson, E.L., Numerical methods in finite element analysis, (1976), Prentice-Hall Englewood Cliffs, N.J · Zbl 0528.65053
[7] {\scT. B. Belytschko and J. M. Kennedy}, Computer models for subassembly simulation, preprint.
[8] {\scM. Bercovier and M. Engelman}, J. Comput. Phys., in press.
[9] Brandt, A., Multi-level adaptive techniques (MLAT) for partial differential equations: ideas and software, () · Zbl 0407.68037
[10] ()
[11] Burggrae, O.R., J. fluid mech., 24, 113-151, (1966)
[12] Christie, I.; Griffiths, D.F.; Mitchell, A.R.; Zienkiewicz, O.C., Int. J. num. methods eng., 10, 1389-1396, (1976) · Zbl 0342.65065
[13] {\scA. T. Chwang}, J. Fluid Mech., {\bf87}, in press.
[14] {\scA. T. Chwang and G. W. Housner}, J. Fluid Mech., {\bf87} in press.
[15] Dennis, S.C.R.; Walker, J.D.A., J. fluid mech., 48, 771-789, (1971)
[16] Falk, R.S., An analysis of the penalty method and extrapolation for the stationary Stokes equations, ()
[17] Felippa, C.A., Comput. struct., 5, 13-29, (1975)
[18] Felippa, C.A., Int. J. num. methods eng., 11, 709-728, (1977)
[19] {\scC. A. Felippa}, Int. J. Num. Methods Eng., in press.
[20] Fichera, G., Existence theorems in elasticity, () · Zbl 0317.73008
[21] {\scM. Fortin and F. Thomasset}, J. Comput. Phys., in press.
[22] Fried, I., Int. J. solids struct., 10, 993-1002, (1974)
[23] ()
[24] ()
[25] Gartling, D.K., Finite element analysis of viscous incompressible flow, () · Zbl 0325.76036
[26] Gartling, D.K., Recent developments in the use of finite element methods in fluid dynamics, (), 65-92
[27] Gartling, D.K., Int. J. num. methods eng., 12, 187-190, (1978)
[28] Gartling, D.K.; Nickell, R.E.; Tanner, R.I., Int. J. num. methods eng., 11, 1155-1174, (1977)
[29] Goudreau, G.L., A computer module for one-step dynamic response of an axisymmetric or plane linear elastic thin shell, Lawrence livermore laboratory report UCID-17730, (February 1978)
[30] Gresho, P.M.; Lee, R.L.; Sani, R.L., Advection-dominated flows, with emphasis on the consequences of mass lumping, () · Zbl 0442.76067
[31] Gresho, P.M.; Lee, R.L.; Stullich, T.W.; Sani, R.L., Solution of the time-dependent Navier-Stokes equations via F.E.M., ()
[32] Griffiths, D.F., On the approximation of convection problems in fluid dynamics, () · Zbl 0367.76077
[33] Griffiths, D.F.; Lorenz, J., An analysis of the Petrov-Galerkin method applied to a model problem, () · Zbl 0384.76065
[34] Heinrich, J.C.; Huyakorn, P.S.; Zienkiewicz, O.C.; Mitchell, A.R., Int. J. num. methods eng., 11, 131-143, (1977)
[35] Heinrich, J.C.; Marshall, R.S.; Zienkiewicz, O.C., Solution of Navier-Stokes equation by a penalty function finite element method, () · Zbl 0414.76014
[36] Hinton, E., Least squares analysis using finite elements, ()
[37] Hinton, E., J. sound vibr., 46, 465-472, (1976)
[38] Hinton, E.; Owen, D.R.J.; Shantaram, D., Dynamic transient linear and nonlinear behaviour of thick and thin plates, ()
[39] Hinton, E.; Pugh, E.D.L., Some quadrilateral isoparametric finite elements based on Mindlin plate theory, (), 851-858
[40] Hinton, E.; Razzaque, A.; Zienkiewicz, O.C.; Davies, J.D., (), 43-65
[41] {\scE. Hinton and N. Bicanic}, Comput Struct., in press.
[42] Hirt, C.W.; Ramshaw, J.D.; Stein, L.R., Numerical simulation of three-dimensional flow past bluff bodies, Los alamos scientific laboratory, report LA-OR-77-1420, (1977), Los Alamos, New Mexico
[43] Hughes, T.J.R., J. appl. mech., 44, 181-183, (1977)
[44] Hughes, T.J.R., Int. J. num. methods eng., 12, 1359-1365, (1978)
[45] Hughes, T.J.R.; Atkinson, J., A variational basis for “upwind” finite elements, ()
[46] Hughes, T.J.R.; Cohen, M., Comput. struct., 9, 445-450, (1978)
[47] Hughes, T.J.R.; Malkus, D.S., On the equivalence of mixed finite element methods with reduced/selective integration displacement methods, (), 23-32
[48] Hughes, T.J.R.; Cohen, M.; Haroun, M., Nucl. eng. des., 46, 203-222, (1978)
[49] Hughes, T.J.R.; Liu, W.K.; Zimmerman, T., Lagrangian-Eulerian finite element formulation for incompressible, viscous flows, ()
[50] Hughes, T.J.R.; Taylor, R.L.; Kanoknukulchai, W., Int. J. num. methods eng., 11, 1529-1543, (1977)
[51] Hughes, T.J.R.; Taylor, R.L.; Levy, J.F., A finite element method for incompressible viscous flows, () · Zbl 0442.76027
[52] Hughes, T.J.R.; Taylor, R.L.; Levy, J.F., High Reynolds number, steady, incompressible flows by a finite element method, () · Zbl 0442.76027
[53] Hughes, T.J.R.; Taylor, R.L.; Sackman, J.L., Finite element formulation and solution of contact-impact problems in continuum mechanics—III, ()
[54] Hughes, T.J.R.; Taylor, R.L.; Sackman, J.L.; Kanoknukulchai, W., Finite element formulation and solution of contact-impact problems in continuum mechanics—IV, ()
[55] Von Karman, T., Trans. amer. soc. civil eng., 98, 418-433, (1933)
[56] Lee, R.L.; Gresho, P.M.; Sani, R.L., Numerical smoothing techniques applied to some finite element solutions of the Navier-Stokes equations, () · Zbl 0446.76034
[57] see also: Int. J. Num. Methods Eng., in press.
[58] Macagno, E.O.; Hung, T.K., J. fluid mech., 28, 43-67, (1967)
[59] Malkus, D.S., Finite element analysis of incompressible solids, () · Zbl 0472.73088
[60] Malkus, D.S., Int. J. solids struct., 12, 731-738, (1976)
[61] Malkus, D.S.; Hughes, T.J.R., Comput. methods appl. mech. eng., 15, 63-81, (1978)
[62] Merger, B., Solution of the limit load problem via the finite element method, (), 445-454
[63] Mitchell, A.R.; Griffiths, D.F., Generalized Galerkin methods for second order equations with significant first derivative terms, (), 90-104 · Zbl 0443.65082
[64] Mitchell, A.R.; Griffiths, D.F., Semi-discrete generalized Galerkin methods for timedependent conduction-convection problems, () · Zbl 0443.65083
[65] Mondkar, D.P.; Powell, G.H., Comput. struct., 4, 531-548, (1974)
[66] Mondkar, D.P.; Powell, G.H., Comput. struct., 4, 699-728, (1974)
[67] Nagtegaal, J.C.; Parks, D.M.; Rice, J.R., Comput. methods appl. mech. eng., 4, 153-178, (1974)
[68] Naylor, D.J., Int. J. num. methods eng., 8, 443-460, (1974)
[69] Olson, M.D.; Tuann, S.Y., Primitive variables versus stream function finite element solutions of the Navier-Stokes equations, () · Zbl 0442.76031
[70] Park, K.C., An implicit, variable-step technique for fluid dynamics problems, (), 33-39 · Zbl 0442.76040
[71] Pracht, W.E.; Brackbill, J.U., 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, (August 1976), Los Alamos, New Mexico
[72] Preprints of the second international symposium on finite element methods in flow problems, (June 14-18, 1976), S. Margherita Ligure Italy
[73] Pugh, E.D.L., The static and dynamic analysis of Mindlin plates by isoparametric finite elements, ()
[74] Pugh, E.D.L.; Hinton, E.; Zienkiewicz, O.C., Int. J. num. methods eng., 12, 1059-1079, (1978)
[75] Richtmyer, R.D.; Morton, K.W., Difference methods for initial-value problems, (1967), Interscience New York · Zbl 0155.47502
[76] Roache, P.J., Computational fluid dynamics, (1976), Hermosa Albuquerque
[77] Roscoe, D.F., J. inst. math. its appl., 16, 291-301, (1975)
[78] D. F. Roscoe, Linear Algebra Its Appl., {\bf14} 123-130.
[79] Roscoe, D.F., Int. J. num. methods eng., 10, 1299-1308, (1976)
[80] Sharan, S.K.; Gladwell, G.M.L., A method of analyzing dam-reservoir-foundation interaction problems, (), 1417-1427
[81] Smith, S.L.; Brebbia, C.A., (), 235-245
[82] Smith, S.L.; Brebbia, C.A., Appl. math. mod., 1, 266-284, (1977)
[83] Strang, G.; Fix, G.J., An analysis of the finite element method, (1973), Prentice-Hall Englewood Cliffs, N.J · Zbl 0278.65116
[84] Taylor, R.L., Computer procedures for finite element analysis, (), Chap. 24
[85] {\scR. L. Taylor and O. C. Zienkiewicz}, Complementary energy with penalty functions in finite element analysis, preprint. · Zbl 0418.73069
[86] Temam, R., Navier-Stokes equations, (1977), North-Holland Amsterdam · Zbl 0335.35077
[87] Tuann, S.Y.; Olson, M.D., Studies of rectangular cavity flow with Reynolds number by a finite element method, () · Zbl 0442.76031
[88] Wachspress, E.L., Isojacobic crosswind differencing, (), 190-199 · Zbl 0382.65048
[89] Westergaard, H.M., Trans. amer. soc. civil eng., 98, 418-433, (1933)
[90] Wilson, E.L.; Bathe, K.J.; Doherty, W.P., Comput. struct., 4, 363-372, (1974)
[91] {\scE. L. Wilson and H. H. Dovey}, Solution or reduction of equilibrium equations for large complex structural systems, preprint.
[92] Zienkiewicz, O.C., The finite element method, (1977), McGraw-Hill London · Zbl 0435.73072
[93] Zienkiewicz, O.C., Int. J. num. methods eng., 12, 191, (1978)
[94] Zienkiewicz, O.C.; Hinton, E., J. franklin inst., 302, 443-461, (1976)
[95] Zienkiewicz, O.C.; Taylor, R.L.; Too, J.M., Int. J. num. methods eng., 3, 275-290, (1971)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.