Survey of trefftz-type element formulations

Abstract

Under the denomination “Trefftz-type elements” (or T-elements) are grouped finite elements the common feature of which is the use of an assumed internal displacement field which satisfies the governing differential equations of the problem a priori. Though in the past several T-element formulations have been presented, until recently their practical use was limited nearly exclusively to the single one known as the hybrid-Trefftz displacement frame element (HT-D). One of the reasons for this situation was the common but incorrect believe that given a particular internal field, the solution accuracy depends little on the T-element model. The paper surveys the existing and some other yet unpublished T-element formulations and shows on numerical examples concerning the Laplace and Poisson equations that their choice can considerably influence the accuracy. As some of these alternative formulations offer distinctly better results than the HT-D elements, it is evident that their study is not just of an academic interest. All considered T-elements offer distinctly better accuracy and faster p-convergence than the conventional p-elements.