SURVEY OF TREFFTZ-TYPE ELEMENT FORMULATIONS

Under the denomination ''Trefftz-type elements'' (or T-elements) are g rouped finite elements the common feature of which is the use of an as sumed internal displacement held which satisfies the governing differe ntial equations of the problem a priori. Though in the past several T- element formulations have been presented, until recently their practic al use was limited nearly exclusively to the single one known as the h ybrid-Trefftz displacement frame element (HT-D). One of the reasons fo r this situation was the common but incorrect believe that given a par ticular internal held, the solution accuracy depends little on the T-e lement model. The paper surveys the existing and some other yet unpubl ished T-element formulations and shows on numerical examples concernin g the Laplace and Poisson equations that their choice can considerably influence the accuracy. As some of these alternative formulations off er distinctly better results than the HT-D elements, it is evident tha t their study is not just of an academic interest. All considered T-el ements offer distinctly better accuracy and faster p-convergence than the conventional p-elements. (C) 1997 Elsevier Science Ltd.