Abstract: Lowest order finite element approximations of time-harmonic wave problems suffer from the pollution effect. That is, as the wavenumber increases, the gap between finite element error and best-approximation widens. For many problems (including heterogeneous Helmholtz equations and even Maxwell's equations with constant scalar coefficients) it is known that hp-FEM suppresses pollution, provided that the discrete spaces satisfy a certain scale-resolution condition.
In this talk we present an analogous result for the time-harmonic Maxwell's equations with piecewise analytic coefficients and impedance boundary conditions. We start by studying the pollution effect in more detail before sketching the proof of our main result, namely that hp-FEM with sufficient scale-resolution suppresses pollution. In addition, we present numerical experiments that validate our findings.
Wavenumber-explicit hp-FEM for Maxwell's equations in piecewise smooth media
29.05.2024 15:30 - 16:00
Organiser:
SFB 65
Location:
HS 2, EG, OMP 1
Location:
und Zoom
Verwandte Dateien
- pde_afternoon_2024-05-29.pdf 930 KB