Galerkin Finite-Element Methods

  • C. A. J. Fletcher
Part of the Springer Series in Computational Physics book series (SCIENTCOMP)


The Galerkin finite-element method has been the most popular method of weighted residuals, used with piecewise polynomials of low degree, since the early 1970s. The rise in the popularity of the Galerkin formulation and the concurrent decline in popularity of the variational finite-element formulation has coincided with the diversification of the finite-element method into areas remote from the structural birthplace of the method.


Shape Function Galerkin Method Trial Function Triangular Element Linear Element 
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  1. Adam, Y. J. Comp. Phys. 24, 10–22 (1977).MathSciNetADSMATHCrossRefGoogle Scholar
  2. Arakawa, A. J. Comp. Phys. 1, 119–143 (1960).ADSCrossRefGoogle Scholar
  3. Astley, R. J., and Eversman, W. J. Sound Vib. 74, 103–121 (1981).ADSMATHCrossRefGoogle Scholar
  4. Astley, R. J., and Eversman, W. “Acoustic Transmission in Lined Ducts”, in Finite Elements in Fluids (ed. R. H. Gallagher), Vol. 4, Wiley, London (1982).Google Scholar
  5. Baker, A. J., and Manhardt, P. D. AIAA J. 16, 807–814 (1978)ADSMATHCrossRefGoogle Scholar
  6. Baker, A. J., and Soliman, M. O. J. Comp. Phys. 32, 289–324 (1979).MathSciNetADSMATHCrossRefGoogle Scholar
  7. Bathe, K.-J., and Wilson, E. L. Numerical Methods in Finite Element Analysis, Prentice-Hall, Englewood Cliffs, NJ (1976).MATHGoogle Scholar
  8. Birkhoff, G., and de Boor, C. R. In Approximations of Functions (ed. H. L. Garabedian ), pp. 164–190 Elsevier (1965).Google Scholar
  9. Bramble, J. H., and Schatz, A. H. Math. Comp. 31, 94–111 (1977).MathSciNetMATHCrossRefGoogle Scholar
  10. Brebbia, C. A. The Boundary Element Method for Engineers, Pentech Press, London (1978)Google Scholar
  11. Ciment, M., Leventhal, S. H., and Weinberg, B. C. J. Comp. Phys. 28, 135–166 (1978)MathSciNetADSMATHCrossRefGoogle Scholar
  12. Culham, W. E., and Varga, R. S. Soc. Pet. Eng. J. 11, 374–388 (1971).Google Scholar
  13. Cullen, M. J. P., and Hall, C. D. Quart, J. R. Met. Soc. 105, 571–592 (1979).ADSCrossRefGoogle Scholar
  14. Cullen, M. J. P., and Morton, K. W. J. Comp. Phys. 34, 245–267 (1980).MathSciNetADSMATHCrossRefGoogle Scholar
  15. Cushman, J. H. I. J. Num. Meth. Eng. 14, 1643–1651 (1979).MathSciNetMATHCrossRefGoogle Scholar
  16. Cushman, J. H. I. J. Num. Meth. Eng. 17, 975–989 (1981).MathSciNetMATHCrossRefGoogle Scholar
  17. Davis, R. T., and Rubin, S. G. Comp. and Fluids 8, 101–132 (1980).MathSciNetMATHCrossRefGoogle Scholar
  18. Dennis, S. C. R., and Walker, J. D. A. J. Fluid Mech. 48, 771–789 (1971).ADSMATHCrossRefGoogle Scholar
  19. Dougalis, V. A., and Serbin, S. M. SIAM J. Num. Anal. 17, 431–446 (1980).MathSciNetADSMATHCrossRefGoogle Scholar
  20. Douglas, J., and Dupont, T. Numer. Math. 22, 99–109 (1974).MathSciNetMATHCrossRefGoogle Scholar
  21. Dupont, T. SIAM J. Num. Anal. 10, 880–889 (1973).MathSciNetADSMATHCrossRefGoogle Scholar
  22. Ergatoudis, J. G., Irons, B. M., and Zienkiewicz, O. C. Int. J. Solids Structures 4, 31–42 (1968)MATHCrossRefGoogle Scholar
  23. Fairweather, G. Finite Element Galerkin Methods for Differential Equations, Dekker, New York (1978).MATHGoogle Scholar
  24. Fletcher, C. A. J. The Application of the Finite Element Method to Two-Dimensional Inviscid Flow. WRE-TN-1606, Salisbury, South Australia (1976).Google Scholar
  25. Fletcher, C. A. J. Improved Integration Techniques for Fluid Flow Finite Element Formulations. WRE-TR-1810, Salisbury, South Australia (1977).Google Scholar
  26. Fletcher, C. A. J. “Burgers’ Equation: A Model for All Reasons”, in Numerical Solution of Partial Differential Equations (ed. J. Noye ), pp. 139–225, North-Holland, Amsterdam (1982a).Google Scholar
  27. Fletcher, C. A. J. “A Comparison of the Finite Element and Finite Difference Methods for Computational Fluid Dynamics”, in Finite Element Flow Analysis (ed. T. Kawai ), pp. 1003–1010, Univ. of Tokyo Press, (1982b).Google Scholar
  28. Gartling, D. K. Comp. Meth. App. Mech. Eng. 12, 365–382 (1977).MathSciNetMATHCrossRefGoogle Scholar
  29. Gartling, D. K. “A Finite Element Analysis of Volumetrically Heated Fluids in an Axisymmetric Enclosure”. 3rd Finite Element in Flow Problems Conference, Banff, Canada, pp. 174–182 (1980).Google Scholar
  30. Gray, W. G., and Pinder, G. F. I. J. Num. Meth. Eng. 10, 893–923 (1976)MathSciNetMATHCrossRefGoogle Scholar
  31. Grotkop, G. Comp. Meth. Appl. Mech. Eng. 2, 147–157 (1973).MATHCrossRefGoogle Scholar
  32. Heubner, K. H. The Finite Element Method for Engineers, Wiley, New York (1975).Google Scholar
  33. Hughes, T. J. R., Taylor, R. L., and Levy, J. F. In Finite Elements in Fluids (ed. R. H. Gallagher et al.), Vol. 3, pp. 55–72, Wiley, London (1978).Google Scholar
  34. Hughes, T. J. R., Liu, W. K., and Brooks, A. J. Comp. Phys. 30, 1–60 (1979)MathSciNetADSMATHCrossRefGoogle Scholar
  35. Irons, B. M. Int. J. Num. Meth. Eng. 2, 5–32 (1970).ADSMATHCrossRefGoogle Scholar
  36. Irons, B. M., and Razzaque, A. In The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations (ed. A. K. Aziz ), pp. 557–587, Academic Press, (1972).Google Scholar
  37. Irons, B., and Ahmad, S. Techniques of Finite Elements, Wiley, Chichester (1980).Google Scholar
  38. Isaacson, E., and Keller, W. B. An Analysis of Numerical Methods, Wiley, New York (1966)Google Scholar
  39. Jennings, A. Matrix Computation for Engineers and Scientists, Wiley, London (1977)MATHGoogle Scholar
  40. Jespersen, D. C. J. Comp. Phys. 16, 383–390 (1974).MathSciNetADSMATHCrossRefGoogle Scholar
  41. Kawahara, M., Takeuchi, N., and Yoshida, T. Int. J. Num. Meth. Eng. 12, 331–351 (1978)MATHCrossRefGoogle Scholar
  42. Khosla, P. K., and Rubin, S. G. J. Eng. Math. 13, 127–141 (1979).MATHCrossRefGoogle Scholar
  43. Mikhlin, S. G. Variational Methods in Mathematical Physics, Pergamon, Oxford (1964).MATHGoogle Scholar
  44. Mitchell, A. R., and Wait, R. The Finite Element Method in Partial Differential Equations, Wiley, London (1977).MATHGoogle Scholar
  45. Norrie, D., and de Vries, G. Finite Element Bibliography, Plenum, New York (1976)MATHCrossRefGoogle Scholar
  46. Oden, J. T. Finite Elements of Nonlinear Continua, McGraw-Hill, New York (1972).MATHGoogle Scholar
  47. Oden, J. T., and Reddy, J. N. An Introduction to the Mathematical Theory of Finite Elements, Wiley, New York (1976a).MATHGoogle Scholar
  48. Oden, J. T., and Reddy, J. N. SIAM J. Num. Anal. 13, 393–404 (1976b).MathSciNetADSMATHCrossRefGoogle Scholar
  49. Oden, J. T. “Penalty Methods and Selective Reduced Integration for Stokesian Flows”, in 3rd Finite Element in Flow Problems Conference, Banff, Canada, pp. 140–145 (1980).Google Scholar
  50. Phuoc, H. B., and Tanner, R. I. J. Fluid Mech. 98, 253–271 (1980).ADSMATHCrossRefGoogle Scholar
  51. Pinder, G. F., and Gray, W. G. Finite Element Simulation in Surface and Subsurface Hydrology, Academic Press, New York (1977).Google Scholar
  52. Richtmyer, R., and Morton, K. W. Difference Methods for Initial-Value Problems, Wiley, New York, 2nd Edn (1967).Google Scholar
  53. Rubbert, P. E., and Saaris, G. R. Review and Evaluation of a Three-Dimensional Lifting Potential Flow Analysis Method for Arbitrary Configurations. AIAA Paper 72–188 (1972).Google Scholar
  54. Schreker, G. O., and Maus, J. R. Noise Characteristics of Jet-flap Type Exhaust Flows. NASA CR-2342 (1974).Google Scholar
  55. Schultz, M. Spline Analysis, Prentice-Hall, Englewood Cliffs, NJ (1973)MATHGoogle Scholar
  56. Showalter, R. E. SIAM J. Num. Anal. 12, 456–463 (1975).MathSciNetADSMATHCrossRefGoogle Scholar
  57. Staniforth, A. N. “A Review of the Applications of the Finite Element Method to Meteorological Flows,” in Finite Element Flow Analysis (ed. T. Kawai) Univ. of Tokyo Press, Tokyo (1982), pp. 835–842.Google Scholar
  58. Staniforth, A. N., and Daley, R. W. Mon. Weath. Rev. 107, 107–121 (1979).ADSCrossRefGoogle Scholar
  59. Strang, G., and Fix, G. J. An Analysis of the Finite Element Method, Prentice-Hall, Englewood Cliffs, NJ (1973).MATHGoogle Scholar
  60. Swartz, B., and Wendroff, B. Math. Comp. 23, 37–50 (1969)MathSciNetMATHCrossRefGoogle Scholar
  61. Taylor, C., and Davis, J. Comp. and Fluids 3, 125–148 (1975).MathSciNetMATHCrossRefGoogle Scholar
  62. Taylor, C. “The Utilisation of the F. E. M. in the Solution of Some Free Surface Problems”, in 3rd Finite Element in Flow Problems Conference, Banff, Canada, pp. 54–81 (1980).Google Scholar
  63. Temam, R., and Thomasset, F. “Numerical Solution of the Navier-Stokes Equations by a Finite Element Method”, in 2nd Finite Element in Flow Problems Conference, St. Margharita Ligure, Italy (1976).Google Scholar
  64. Temam, R. “Some Finite Element Methods in Fluid Flow”, in Lecture Notes in Physics, No. 90, pp. 34–55 Springer-Verlag, Berlin, (1979a).Google Scholar
  65. Temam, R. Navier-Stokes Equations, North-Holland, Amsterdam (1979b).MATHGoogle Scholar
  66. Thomée, V. Math. Comp. 31, 652–660 (1977).MathSciNetMATHCrossRefGoogle Scholar
  67. Tuann, S.-Y., and Olson, M. D. J. Comp. Phys. 29, 1–19 (1978).MathSciNetADSMATHCrossRefGoogle Scholar
  68. Wellford, L. C., and Oden, J. T. Comp. Meth. App. Mech. Eng. 5, 83–96 (1975)MathSciNetMATHCrossRefGoogle Scholar
  69. Wheeler, M. F. SIAM J. Num. Anal. 10, 723–759 (1973).ADSCrossRefGoogle Scholar
  70. Whiteman, J. R. A Bibliography for Finite Elements, Academic Press (1975)MATHGoogle Scholar
  71. Zienkiewicz, O. C. The Finite Element Method, McGraw-Hill, London, 3rd Edn. (1977).MATHGoogle Scholar

Copyright information

© Springer-Verlag New York Inc. 1984

Authors and Affiliations

  • C. A. J. Fletcher
    • 1
  1. 1.Department of Mechanical EngineeringUniversity of SydneyAustralia

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