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Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations

Brooks, Alexander N., Hughes, Thomas J.R.·1982·Computer Methods in Applied Mechanics and Engineering
DOI 10.1016/0045-7825(82)90071-8
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Research works printed but not linked: 34

  1. Baker, 1979, Research on numerical algorithms for the three-dimensional Navier-Stokes equations, Part I. Accuracy, convergence and efficiency, Tech. Rep. AFFDL-TR-79-3141
  2. Chorin, 1968, Numerical solution of the Navier-Stokes equations, Math. Comp., 22, 745, 10.1090/S0025-5718-1968-0242392-2 · DOI · Paper page
  3. Christie, 1976, Finite element methods for second order differential equations with significant first derivatives, Internat. J. Numer. Methods Engrg., 10, 1389, 10.1002/nme.1620100617 · doi:10.1002/nme.1620100617
  4. Dendy, 1974, Two methods of Galerkin type achieving optimum L2 rates of convergence for first order hyperbolics, SIAM J. Numer. Anal., 11, 637, 10.1137/0711052 · doi:10.1137/0711052
  5. Davis, 1976, An evaluation of upwind and central difference approximations by a study of recirculating flow, Computers and Fluids, 4, 29, 10.1016/0045-7930(76)90010-4 · doi:10.1016/0045-7930(76)90010-4
  6. Donea, 1979, Accurate explicit finite element schemes for convective-conductive heat transfer problems, Vol. 34
  7. Gresho, 1981, Solution of the time dependent, three-dimensional incompressible Navier-Stokes equations via FEM, Lawrence Livermore Laboratory Report UCRL-85337
  8. Gresho, 1978, Advection-dominated flows, with emphasis on the consequences of mass lumping, Vol. 3
  9. Gresho, 1979, Don't suppress the wiggles—They're telling you something!, Vol. 34
  10. Gresho, 1979, Solution of the time dependent incompressible Navier-Stokes and Boussinesq equations using the Galerkin finite element method, Lawrance Livermore Laboratory Rep. UCRL-82899
  11. Gresho, 1980, On the time-dependent solution of the Navier-Stokes equations in two and three dimensions, Vol. 1, 27
  12. Griffiths, 1979, On generating upwind finite element methods, Vol. 34
  13. Heinrich, 1977, An ‘upwind’ finite element scheme for two-dimensional convective transport equation, Intern. J. Numer. Methods Engrg., 11, 134
  14. Heinrich, 1979, The finite element method and ‘upwinding’ techniques in the numerical solution of convection dominated flow problems, Vol. 34
  15. Hughes, 1978, A simple scheme for developing ‘upwind’ finite elements, Internat. J. Numer. Methods Engrg., 12, 1359, 10.1002/nme.1620120904 · doi:10.1002/nme.1620120904
  16. Hughes, 1980, Recent developments in computer methods for structural analysis, Nucl. Engrg. Des., 57, 427, 10.1016/0029-5493(80)90116-8 · doi:10.1016/0029-5493(80)90116-8
  17. Hughes, 1979, A multidimensional upwind scheme with no crosswind diffusion, Vol. 34
  18. 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).
  19. Hughes, 1979, Review of finite element analysis of incompressible viscuous flows by the penalty function formulation, J. Comput. Phys., 30, 1, 10.1016/0021-9991(79)90086-X · DOI
  20. Hughes, 1979, Implicit-explicit finite elements in nonlinear transient analysis, Comput. Meths. Appl. Mech. Engrg., 17/18, 159, 10.1016/0045-7825(79)90086-0 · doi:10.1016/0045-7825(79)90086-0
  21. Hughes, 1978, High Reynolds number, steady, incompressible flows by a finite element method, Vol. 3
  22. Kelly, 1980, A note of upwinding and anisotropic balancing dissipation in finite element approximations to convective diffusion problems, Internat. J. Numer. Methods Engrg., 15, 1705, 10.1002/nme.1620151111 · doi:10.1002/nme.1620151111
  23. Lee, 1979, Smoothing techniques for certain primitive variable solutions of the Navier-Stokes equations, Internat. J. Numer. Methods Engrg., 14, 1785, 10.1002/nme.1620141204 · doi:10.1002/nme.1620141204
  24. Leonard, 1979, A survey of finite differences of opinion on numerical muddling of the incomprehensible defective confusion equation, Vol. 34
  25. Leonard, 1980, Note on the Von Neumann stability of the explicit FTCS convective diffusion equation, Appl. Math. Modelling, 4, 401, 10.1016/0307-904X(80)90168-7 · doi:10.1016/0307-904x(80)90168-7
  26. Raithby, 1976, A critical evaluation of upstream differencing applied to problems involving fluid flow, Comput. Meths. Appl. Mech. Engrg., 75, 10.1016/0045-7825(76)90078-5 · DOI · Paper page
  27. Raithby, 1974, Upstream-weighted differencing schemes and their application to elliptic problems involving fluid flow, Comput. and Fluids, 2, 191, 10.1016/0045-7930(74)90013-9 · DOI
  28. Raymond, 1976, Selective damping in a Galerkin method for solving wave problems with variable grids, Monthly Weather Rev., 104, 1583, 10.1175/1520-0493(1976)104<1583:SDIAGM>2.0.CO;2 · doi:10.1175/1520-0493(1976)104<1583:sdiagm>2.0.co;2
  29. Sani, 1981, On the solution of the time-dependent incompressible Navier-Stokes equations via a penalty Galerkin finite element method, Lawrance Livermore Laboratory Rept. UCRL-85354
  30. Sani, 1981, The cause and cure of the spurious pressures generated by certain GFEM solutions of the incompressible Navier-Stokes equations, Internat. J. Numer. Meths. Fluids
  31. Smith, 1977, Improved stability techniques for the solution of Navier-Stokes equations, Appl. Math. Modelling, 1, 226, 10.1016/0307-904X(77)90013-0 · doi:10.1016/0307-904x(77)90013-0
  32. T.E. Tezduyar, Ph.D. Thesis, California Institute of Technology, in preparation.
  33. 1978, Vol. 630, 190
  34. Zienkiewicz, 1978, The finite element method and convection problems in fluid mechanics, Vol. 3, 1

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Metadata

Authors
Brooks, A. N., & Hughes, T. J. R.
Venue
Computer Methods in Applied Mechanics and Engineering
Publisher
Elsevier BV
Published
1982-09
Volume
32
Issue
1-3
Pages
199-259
ISSN
0045-7825 (ISSN-L)
DOI
10.1016/0045-7825(82)90071-8
OpenAlex
W2073897969
Cited by
5,332
References
0
FWCI
21.31
Type
journal article
Language
en
Open access
closed
Licence
www.elsevier.com/tdm/userlicense/1.0/ (tdm)

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CoChat. (2026). Citation check: Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. https://app.cochat.ai/papers/10.1016/0045-7825(82)90071-8
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Brooks, A. N., & Hughes, T. J. R. (1982). Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering. https://doi.org/10.1016/0045-7825(82)90071-8

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