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The convergence of Rayleigh-Ritz approximations

  • M. J. O'Carroll (a1) and P. E. Lush (a1)

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This paper is concerned with the convergence of Rayleigh-Ritz approximations to the solution of an elliptic boundary value problem. Although the work arose in connection with the aerofoil problem (and it is to this problem that the results obtained are immediately applied), the methods here employed are suitable for use on the wider class of problem mentioned above.

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References

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[1]Lush, P. E. and Cherry, T. M., ‘The variational method in hydrodynamics’, Quart. J. Mech. and Appl. Math. 9. (1956), 621.
[2]Lush, P. E., ‘The convergence of Rayleigh-Ritz approximations in hydrodynamics’, J. Aust. Math. Soc. 3 (1963), 99103.
[3]Morrey, C. B., Problems in the Calculus of Variations and Related Topics (Univ. of Calif. Publ. in Math. 1, 1943).
[4]Shiffman, M., ‘On the existence of subsonic flows of a compressible fluid’, J. Rat. Mech. and Anal. 1 (1952), 605652.
[5]Priwalow, I. I., Einführung in die Functionentheorie (Teil II B. G. Teubner Verlag, 1959).
[6]Estermann, T., ‘Über die totale Variation einer stetigen Funktion und den Cauchyschen Integralsatz’, Math. Zeitschrift 37 (1933), 556–60.
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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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