FEM with Trefftz trial functions on polyhedral elements

The goal of this paper is to generalize the BEM-based FEM for second order elliptic boundary value problems to three space dimensions with the emphasis on polyhedral meshes with polygonal faces, where even nonconvex elements are allowed. Due to an implicit definition of the trial functions, the strategy yields conforming approximations and is very flexible with respect to the meshes. Thus, it gets into the line of recent developments in several areas. The arising local problems are treated by two dimensional Galerkin schemes coming from finite and boundary element formulations. With the help of a new interpolation operator and its properties, convergence estimates are proven in the H1as well as in the L2-norm. Numerical experiments confirm the theoretical results.