Boundary Element based Treﬀtz Methods for Potential Problems
Dr. Clemens HofreitherOct. 27, 2009, 12:45 p.m. T 112
We present a Treﬀtz method employing locally harmonic ansatz functions for the solution of potential equations in two- or three-dimensional domains.
The method supports heterogeneous meshes consisting of various nonstandard polygonal/polyhedral element shapes, as well as grids with hanging nodes. In the special case of a conforming triangular (in 2-D) or tetrahedral (in 3-D) mesh, the method is equivalent to the corresponding nodal finite element method with piecewise linear and continuous ansatz functions.
Using element-local Steklov-Poincaré operators, the formulation is reduced to the mesh skeleton consisting of the union of the boundaries of all elements. Boundary element discretization is then employed in order to obtain a numerical scheme. We give error estimates and present first numerical results.