Modul: MAT870 Zurich Colloquium in Applied and Computational Mathematics

## Asymptotically optimal a priori and a posteriori error estimates for edge finite element discretizations of time-harmonic Maxwell's equations

Talk by Dr. Théophile Chaumont-Frelet

Speaker invited by: Prof. Dr. Stefan Sauter

**Date:** 11.10.23 **Time:** 16.30 - 17.30 **Room:** ETH HG E 1.2

'Time-harmonic Maxwell's equations model the propagation of
electromagnetic waves, and their numerical discretization
by finite elements is instrumental in a large array of applications.
In the simpler setting of acoustic waves, it is known that (i) the Galerkin
Lagrange finite element approximation to a Helmholtz problem becomes
asymptotically optimal as the mesh is refined. Similarly, (ii)
asymptotically constant-free a posteriori error estimates are available
for Helmholtz problems. In this talk, considering Nédélec finite element
discretizations of time-harmonic Maxwell's equations, I will show that

(i) still holds true and propose an a posteriori error estimator providing

(ii). Both results appear to be novel contributions to the existing
literature.'''