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Convergence Analysis for Finite Element Discretizations of Highly Indefinite Helmholtz Problems

Stefan Sauter
University of Zurich, visiting UCSD


A rigorous convergence theory for Galerkin methods for a model Helmholtz problem in R^{d}, d=1,2,3, is presented. General conditions on the approximation properties of the approximation space are stated that ensure quasi-optimality of the method. As an application of the general theory, a full error analysis of the classical hp-version of the finite element method (hp-FEM) is presented where the dependence on the mesh width h, the approximation order p, and the wave number k is given explicitly. In particular, it is shown that quasi-optimality is obtained under the conditions that kh/p is sufficiently small and the polynomial degree p is at least O(log k). This result improves existing stability conditions substantially.

Tuesday, October 25, 2011
11:00AM AP&M 2402