Trefftz in translation
Abstract
This paper reviews the important concepts presented by Trefftz in 1926 regarding bounds to solutions, error estimation, and hybrid fields for use with domain decomposition. Observations are offered from the perspective of today's relatively mature state of the art in finite element methods. The numerical examples presented by Trefftz are also reviewed with the benefit of 'exact' solutions made available from current commercial finite element methods. The accuracies of the solutions given by Trefftz are quantified and compared, and the effectivity indices of Trefftz's proposed error estimates are also quantified. An English translation of the original German version of Trefftz's paper is included for reference in an Appendix.
Keywords
References
[1] E. Trefftz. Ein gegenstuck zum ritzschen verfahren. In: Proceedings of the 2nd International Congress of Applied Mechanics, Orell Fussli Verlag., pages 131-137, Zurich, 1926.[2] E. Stein. An appreciation of Erich Trefftz. Compo Ass. Mech. and Eng. Sci. , 4: 301- 304, 1997.
[3] B. M. Fraeijs de Veubeke. Stress Analysis, chapter 9: Displacement and equilibrium models in the finite element method. Wiley, New York, 1965.
[4] M. Ainsworth, J . T. Oden. A posteriori error estimation in finite element analysis. Wiley, New York, 2000.
[5] O. J . B. A. Pereira, J. P. M. Almeida. Adaptive refinement for a local error bound based on duality. In: 3rd International Workshop/ Euro Conference on Trefftz Methods, Exeter, 2002.
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