Past Event: Oden Institute Seminar

Wave-Number Explicit Error Estimates for the Galerkin Discretization of Maxwell's Equation

Stefan Sauter, Professor-Dr., Institut für Mathematik, Universität Zürich

Abstract

In our talk we consider the numerical solution of the electric Maxwell equation by hp finite element methods. We will derive error estimates which are explicit in the mesh size h, the local polynomial degree p of the finite elements, and the wave number k. The stability analysis requires the combination of frequency splittings with Helmholtz and Hodge decompositions and the derivation of k-explicit estimates for three types of dual problems. We will explain the proof of the main result: The Galerkin discretization is pollution free provided the resolution condition: p>= C1 log k and k h/p <= C2 is satisfied for some constants C1 and C2. Bio: Prof.Dr. Sauter, completed his Habilitation in Mathematics in 1997, and received his Doctorate in 1993. He has been a Full professor for “Angewandte Mathematik”, Universität Zürich since 1999. Previously he worked at the Universität Leipzig. His awards include: 1981 First prize, Bundeswettbewerb Mathematik; 1988-1990 Stipend of the “Studienstiftung des Deutschen Volkes”; 1993-1994 Stipend of the German research foundation; 1996 Oberwolfach Prize in “Applied Mathematics”; and 2000 Reprint of the paper “Is the pollution effect of the FEM avoidable for the Helmholtz equation considering high wave numbers” (jointly with I. Babuška) in SIAM Reviews.