Trefftz type approximation and the generalized finite element method - history and development

  • Olgierd C. Zienkiewicz University of Wales Swansea

Abstract

This paper shows the essential unity between the known approximation procedures to differential equations. The boundary type approximations associated with Trefftz are shown to be a particular form of the weighted residual approximation and can provide a very useful basis for generating hybrid 'finite elements'. These can be used in combination with other finite element approaches.

Keywords

References

[1] E. Trefftz. Ein Gegenstuck zum Ritzschen Verfahren. Proc. 2nd Int. Congress of Applied mechanics, Zürich, 1926.
[2] O.C. Zienkiewicz, D.W. Kelly and P. Bettes. The coupling of the finite element method and boundary solution procedures. Int. 1. Numer. Meth. Eng. , 11(2): 355- 375, 1977.
[3] O.C. Zienkiewicz, D.W. Kelly and P. Bettes. Marriage à la mode - the best of both worlds (finite elements and boundary integrals). In: R. Glowinski et al., eds., Energy Methods in Finite Element Analysis, Chapter 5, p.8l. J. Wiley & Son, 1979.
[4] Ch. Massonet. Numerical Use ofIntegral Procedures. In: O.C. Zienkiewicz and G.S. Holister, eds., Stress Analysis, Ch. 10, 198- 235. J. Wiley & Son, 1965.
[5] M.A. Jaswon. Integral Equation Methods in Potential Theory; I. Proc. Roy. Soc., Series A, 275: 23-32, 1963.
Published
Jun 15, 2023
How to Cite
ZIENKIEWICZ, Olgierd C.. Trefftz type approximation and the generalized finite element method - history and development. Computer Assisted Methods in Engineering and Science, [S.l.], v. 4, n. 3-4, p. 305-316, june 2023. ISSN 2956-5839. Available at: <https://cames.ippt.gov.pl/index.php/cames/article/view/1374>. Date accessed: 03 dec. 2024.
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Vol 4 No 3-4 (1997)
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Articles
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