Abstract
In the preceding chapters we have examined the structure and properties of the traditional Galerkin method and observed that its modern developments have gone in two radically different directions. First, finite-element methods use local, low-order polynomial trial functions to generate sparse algebraic equations in terms of meaningful nodal unknowns. Secondly the use of global, orthogonal trial functions permits spectral methods to achieve a high accuracy per degree of freedom.
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References
Adam, Y. J. Comp. Phys. 24, 10–22 (1977).
Baker, A. J., and Soliman, M. O. J. Comp. Phys. 32, 289–324 (1979).
Culham, W. E., and Varga, R. S. Soc. Pet. Eng. J. 11, 374–388 (1971).
Deconinck, H., and Hirsch, C. Lecture Notes in Physics, Vol. 141, pp. 138–143, Springer-Verlag, Berlin (1981).
Fix, G. J. SIAM J. App. Math. 29, 371–387 (1975).
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 (1982).
Fletcher, C. A. J., and Fleet, R. W. “A Dorodnitsyn Finite Element Boundary Layer Formula- tion”, 8th International Conference on Numerical Methods in Fluid Dynamics, Aachen, 1982.
Fletcher, C. A. J., and Holt, M. J. Comp. Phys. 18, 154–164 (1975).
Gear, C. W. Numerical Initial Value Problems in Ordinary Differential Equations, Prentice-Hall, Englewood Cliffs, NJ (1971).
Gottlieb, D., and Orszag, S. A. Numerical Analysis of Spectral Methods: Theory and Applications, SIAM, Philadelphia (1977).
Gresho, P. M., Lee, R. L., and Sani, R. L. In Finite Elements in Fluids, Vol. 3, pp. 335–350, Wiley, London (1978).
Haidvogel, D. B., Robinson, A. R., and Schulman, E. E. J. Comp. Phys. 34, 1–53 (1980).
Hopkins, T. R., and Wait, R. Int. J. Num. Meth. Eng. 12, 1081–1107 (1978).
Jameson, A. In Numerical Methods in Fluid Dynamics (eds. H. J. Wirz and J. J. Smolderen ), pp. 1–87, Hemisphere, Washington (1978).
Jespersen, D. C. J. Comp. Phys. 16, 383–390 (1974).
Kreiss, H. O. Lecture Notes in Mathematics, Vol. 363. pp. 64–74, Springer-Verlag, Berlin (1973).
Majda, A., Donoghue, J., and Osher, S. Math. Comp. 32, 1041–1081 (1978).
McCrory, R. L., and Orszag, S. A. J. Comp. Phys. 37, 93–112 (1980).
Morchoisne, Y. La Recherche Aerospatiale 5, 11–31 (1979).
Morton, K. W. In The State of the Art in Numerical Analysis (ed. D. Jacobs), pp. 699–756, Academic Press, London (1977).
Orszag, S. A. J. Fluid Mech. 49, 75–112 (1971).
Orszag, S. A. J. Comp. Phys. 37, 70–92 (1980).
Orszag, S. A., and Israeli, M. Ann. Rev. Fluid Mech. 6, 281–318 (1974).
Patterson, G. S. Ann. Rev. Fluid Mech. 10, 289–300 (1978).
Pinder, G. F., and Gray, W. G. Finite Element Simulation in Surface and Subsurface Hydrology, Academic Press, New York (1977).
Popinski, Z., and Baker, A. J. J. Comp. Phys. 21, 55–84 (1976).
Soliman, M. O., and Baker, A. J. Comp. Fluids 9, 43–62 (1981a).
Soliman, M. O., and Baker, A. J. Comp. Meth. App. Mech. Eng. 28, 81–102 (1981b).
Swartz, B. In Mathematical Aspects of Finite Elements in Partial Differential Equations (ed. C. de Boor ), pp. 279–312 Academic Press, New York (1974).
Swartz, B., and Wendroff, B. SIAM J. Num. Anal. 11, 979–993 (1974).
Thompson, J. F., Thames, F. C. and Mastin, C. W. J. Comp. Phys. 15, 299–319 (1974).
Wigton, L. B., and Holt, M. Viscous—Inviscid Interaction in Transonic Flow, AIAA 5th Computational Fluid Dynamics Conference, Palo Alto, paper 81–1003 (1981).
Zienkiewicz, O. C. The Finite Element Method, 3rd Ed., McGraw-Hill, London (1977).
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Fletcher, C.A.J. (1984). Comparison of Finite-Difference, Finite-Element, and Spectral Methods. In: Computational Galerkin Methods. Springer Series in Computational Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-85949-6_6
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DOI: https://doi.org/10.1007/978-3-642-85949-6_6
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