Aspects of Trefftz' Method in BEM and FEM and their coupling

Abstract

In both boundary element methods and Trefftz-type finite element methods a partial differential equation in some domain is treated by solving a discrete problem on the boundary of the domain and possibly the boundaries between subdomains. We consider a Trefftz element formulation which is based on the complementary energy functional, and we compare different regularizations of the interelement continuity conditions. Also starting from the complementary energy functional, mixed finite elements can be constructed such that the stresses satisfy equilibrium a priori. We describe a coupling of these elements with the by now classical symmetric Galerkin-BEM.