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.