Abstract

The efficient numerical discretization of highly indefinite Helmholtz problems is a challenging task in the simulation of scattering problems. We will present new wave-number explicit convergence results for hpdiscretizations of conventional variational formulations of the Helmholtz problem. The key ingredient in the stability analysis of the finite element discretization is the “splitting lemma”, which splits the regularity of the solution into a “rough” part with “good” regularity constant and into an highly oscillatory, analytic part with more critical regularity constant. We will also discuss in this talk very recent stability results for non-constant wave speed. This talk comprises joint work with M. Melenk and I. Graham.

[Light refreshments will be served outside the venue at 4:00-4:30 pm. Please come and join us.]