Convergence Analysis for a Non-standard Finite Element Method on Polyhedral Meshes

Dr. Clemens Hofreither

April 12, 2011, 4:30 p.m. HS 14

We present a non-standard finite element method based on element-local boundary integral operators. The method is able to treat general polyhedral meshes and employs locally PDE-harmonic trial functions. The new method is applicable to PDEs for which a local fundamental solution within each element is explicitly known. Using the diffusion equation as a model problem, we provide a rigorous error analysis of the method and show convergence rates in both the L2- and H1-norms which are identical to those of a standard finite element method. Some numerical tests confirm these theoretical results.