×

zbMATH — the first resource for mathematics

Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. (English) Zbl 0497.76041

MSC:
76D05 Navier-Stokes equations for incompressible viscous fluids
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Atkinson, J.D.; Hughes, T.J.R., Upwind finite element schemes for convective-diffusive equations, charles kolling laboratory tech. note C-2, (1977), The University of Sydney Sydney, N.S.W
[2] Baker, A.J., Research on numerical algorithms for the three-dimensional Navier-Stokes equations, part I. accuracy, convergence and efficiency, Tech. rep. AFFDL-TR-79-3141, (1979), Wright-Patterson Air Force Base, OH
[3] Brooks, A.; Hughes, T.J.R., Streamline upwind/Petrov-Galerkin methods for advection dominated flows, () · Zbl 0449.76077
[4] Chorin, A.J., Numerical solution of the Navier-Stokes equations, Math. comp., 22, 745, (1968) · Zbl 0198.50103
[5] Christie, I.; Griffiths, D.F.; Mitchell, A.R.; Zienkiewicz, O.C., Finite element methods for second order differential equations with significant first derivatives, Internat. J. numer. methods engrg., 10, 1389-1396, (1976) · Zbl 0342.65065
[6] Dendy, J.E., Two methods of Galerkin type achieving optimum L2 rates of convergence for first order hyperbolics, SIAM J. numer. anal., 11, 637-653, (1974) · Zbl 0293.65077
[7] Davis, G.DeVahl; Mallinson, G., An evaluation of upwind and central difference approximations by a study of recirculating flow, Computers and fluids, 4, 29-43, (1976) · Zbl 0329.76025
[8] J. Donea, Private Communication, 1980.
[9] Donea, J.; Guiliani, S.; Laval, H., Accurate explicit finite element schemes for convective-conductive heat transfer problems, () · Zbl 0423.76068
[10] Gresho, P.M.; Chan, S.T.; Lee, R.L.; Upson, C.D., Solution of the time dependent, three-dimensional incompressible Navier-Stokes equations via FEM, Lawrence livermore laboratory report UCRL-85337, (1981) · Zbl 0506.76022
[11] Gresho, P.; Lee, R.; Sani, R., Advection-dominated flows, with emphasis on the consequences of mass lumping, () · Zbl 0442.76067
[12] Gresho, P.M.; Lee, R.L., Don’t suppress the wiggles—they’re telling you something!, () · Zbl 0436.76065
[13] Gresho, P.M.; Lee, R.L.; Chan, S.T.; Sani, R.L., Solution of the time dependent incompressible Navier-Stokes and Boussinesq equations using the Galerkin finite element method, (), (1979), Also
[14] Gresho, P.M.; Lee, R.L.; Upson, C.D., FEM solution of the Navier-Stokes equations for vortex shedding behind a cylinder: experiments with the four-node element, () · Zbl 0506.76022
[15] Gresho, P.M.; Lee, R.L.; Sani, R.L., On the time-dependent solution of the Navier-Stokes equations in two and three dimensions, (), 27-81 · Zbl 0446.76034
[16] Griffiths, D.F.; Mitchell, A.R., On generating upwind finite element methods, () · Zbl 0423.76069
[17] Heinrich, J.C.; Huyakorn, P.S.; Zienkiewicz, O.C.; Mitchell, A.R., An ‘upwind’ finite element scheme for two-dimensional convective transport equation, Intern. J. numer. methods engrg., 11, 134-143, (1977) · Zbl 0353.65065
[18] Heinrich, J.; Zienkiewicz, O.C., The finite element method and ‘upwinding’ techniques in the numerical solution of convection dominated flow problems, () · Zbl 0436.76062
[19] Hughes, T.J.R., A simple scheme for developing ‘upwind’ finite elements, Internat. J. numer. methods engrg., 12, 1359-1365, (1978) · Zbl 0393.65044
[20] Hughes, T.J.R., Implicit-explicit finite element techniques for symmetric and nonsymmetric systems, () · Zbl 0514.73066
[21] Hughes, T.J.R., Recent developments in computer methods for structural analysis, Nucl. engrg. des., 57, 427-439, (1980)
[22] Hughes, T.J.R.; Atkinson, J., A variational basis for ‘upwind’ finite elements, ()
[23] Hughes, T.J.R.; Brooks, A., A multidimensional upwind scheme with no crosswind diffusion, () · Zbl 0423.76067
[24] Hughes, T.J.R.; Brooks, A., Galerkin/upwind finite element mesh partitions in fluid mechanics, (), 103-112
[25] T.J.R. Hughes and A. Brooks, A. theoretical framework for Petrov-Galerkin methods with discontinuous weighting functions: Application to the streamline upwind procedure, to appear in: R.H. Gallagher, ed., Finite Elements in Fluids, Vol. 4 (Wiley, London).
[26] Hughes, T.J.R.; Liu, W.K.; Brooks, A., Review of finite element analysis of incompressible viscuous flows by the penalty function formulation, J. comput. phys., 30, 1-60, (1979)
[27] Hughes, T.J.R.; Pister, K.S.; Taylor, R.L., Implicit-explicit finite elements in nonlinear transient analysis, Comput. meths. appl. mech. engrg., 17/18, 159-182, (1979) · Zbl 0413.73074
[28] Hughes, T.J.R.; Taylor, R.L.; Levy, J.F., High Reynolds number, steady, incompressible flows by a finite element method, () · Zbl 0442.76027
[29] T.J.R. Hughes and T.E. Tezduyar, Private Communication, 1981.
[30] Johnson, C.; Nävert, U., Analysis of some finite element methods for advection-diffusion problems, () · Zbl 0455.76081
[31] Kelly, D.W.; Nakazawa, S.; Zienkiewicz, O.C.; Heinrich, J.C., A note of upwinding and anisotropic balancing dissipation in finite element approximations to convective diffusion problems, Internat. J. numer. methods engrg., 15, 1705-1711, (1980) · Zbl 0452.76068
[32] Lee, R.L.; Gresho, P.M.; Sani, R.L., Smoothing techniques for certain primitive variable solutions of the Navier-Stokes equations, Internat. J. numer. methods engrg., 14, 1785-1804, (1979) · Zbl 0426.76035
[33] Leonard, B.P., A survey of finite differences of opinion on numerical muddling of the incomprehensible defective confusion equation, () · Zbl 0435.76003
[34] Leonard, B.P., Note on the von Neumann stability of the explicit FTCS convective diffusion equation, Appl. math. modelling, 4, 401, (1980) · Zbl 0443.76049
[35] Morton, K.W.; Barrett, J.W., Optimal finite element methods for diffusion-convection problems, (), 134-148 · Zbl 0455.76088
[36] Oden, J.T., Penalty methods and selective reduced integration for Stokesian flows, () · Zbl 0447.76029
[37] Raithby, G.D., A critical evaluation of upstream differencing applied to problems involving fluid flow, Comput. meths. appl. mech. engrg., 75-103, (1976) · Zbl 0346.76064
[38] Raithby, G.D.; Torrance, K.E., Upstream-weighted differencing schemes and their application to elliptic problems involving fluid flow, Comput. and fluids, 2, 191-206, (1974) · Zbl 0335.76008
[39] Raymond, W.H.; Garder, A., Selective damping in a Galerkin method for solving wave problems with variable grids, Monthly weather rev., 104, 1583-1590, (1976)
[40] Reddy, J.N., On the mathematical theory of penalty-finite elements for Navier-Stokes equations, () · Zbl 0447.76027
[41] Roache, P.J., Computational fluid dynamics, (1976), Hermosa Albuquerque, NM
[42] Sani, R.L.; Eaton, B.E.; Gresho, P.M.; Lee, R.L.; Chan, S.T., On the solution of the time-dependent incompressible Navier-Stokes equations via a penalty Galerkin finite element method, Lawrance livermore laboratory rept. UCRL-85354, (1981) · Zbl 0487.76038
[43] Sani, R.L.; Gresho, P.M.; Lee, R.L., On the spurious pressures generated by certain GFEM solutions of the incompressible Navier-Stokes equations, () · Zbl 0446.76034
[44] Sani, R.L.; Gresho, P.M.; Lee, R.L.; Griffiths, D.F., The cause and cure of the spurious pressures generated by certain GFEM solutions of the incompressible Navier-Stokes equations, Internat. J. numer. meths. fluids, (1981), to appear. · Zbl 0461.76021
[45] Smith, S.L.; Brebbia, C.A., Improved stability techniques for the solution of Navier-Stokes equations, Appl. math. modelling, 1, 226-234, (1977) · Zbl 0362.76002
[46] Taylor, R.L., Computer procedures for finite element analysis, (), Ch. 24
[47] Temam, R., On the theory and numerical analysis of the Navier-Stokes equations, (1977), North-Holland Amsterdam
[48] T.E. Tezduyar, Ph.D. Thesis, California Institute of Technology, in preparation.
[49] Wachspress, E.L., Isojacobic crosswind differencing, (), 190-199 · Zbl 0382.65048
[50] Wahlbin, L.B., A dissipative Galerkin method for the numerical solution of first order hyperbolic equations, (), 147-169
[51] Zienkiewicz, O.C.; Heinrich, J.C., The finite element method and convection problems in fluid mechanics, (), 1-22 · Zbl 0436.76062
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.