9 papers
The pollution effect for FEM approximations of the Ginzburg-Landau equation
Théophile Chaumont-Frelet, Patrick Henning
In this paper, we investigate the approximation properties of solutions to the Ginzburg-Landau equation (GLE) in finite element spaces. Special attention is given to how the errors…
A new family of a posteriori error estimates for non-conforming finite element methods leading to stabilization-free error bounds
T. Chaumont-Frelet
We propose new a posteriori error estimators for non-conforming finite element discretizations of second-order elliptic PDE problems. These estimators are based on novel reformulat…
Sharp error bounds for edge-element discretisations of the high-frequency Maxwell equations
Théophile Chaumont-Frelet, Jeffrey Galkowski, Euan A. Spence
We prove sharp wavenumber-explicit error bounds for first- or second-family-Nédélec-element (a.k.a. edge-element) conforming discretisations, of arbitrary (fixed) order, of the v…
Commuting quasi-interpolators and Maxwell compactness for a polytopal de Rham complex
Théophile Chaumont-Frelet, Jérôme Droniou, Simon Lemaire
We establish Maxwell compactness results for the Discrete De Rham (DDR) polytopal complex: sequences in this polytopal complex with bounded discrete …
Computable Poincaré--Friedrichs constants for the de~Rham complex over convex domains and domains with shellable triangulations
Théophile Chaumont-Frelet, Martin Werner Licht, Martin VohralÃk
We construct potentials for the exterior derivative, in particular, for the gradient, the curl, and the divergence operators, over domains with shellable triangulations. Notably, t…
A ill-posed scattering problem saturating Weyl's law
T. Chaumont-Frelet
This paper focuses on the well-posedness (or lack thereof) of three-dimensional time-harmonic wave propagation problems modeled by the Helmholtz equation. It is well-known that if…