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