14 citations · 25 across the 25 of their papers we have counts for
21 papers · 1 filter
Frequency-explicit convergence analysis of a multiscale finite element method for highly heterogeneous scattering problems
T. Chaumont-Frelet, Z. Kassali
We analyze the numerical approximation of time-harmonic scattering by highly heterogeneous penetrable obstacles. These problems are especially challenging in the high-frequency reg…
An efficient Galerkin method for high-frequency scattering problems using Wilson bases
T. Chaumont-Frelet, M. Ingremeau, F. Proust
We propose a new Galerkin discretization scheme for wave scattering problems that is based on microlocalised basis functions. We show that the proposed method can be made uniformly…
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 Vohralík
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 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…
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 hybridizable discontinuous Galerkin method with transmission variables for time-harmonic acoustic problems in heterogeneous media
Simone Pescuma, Gwénaël Gabard, Théophile Chaumont-Frelet +1
We consider the finite element solution of time-harmonic wave propagation problems in heterogeneous media with hybridizable discontinuous Galerkin (HDG) methods. In the case of hom…
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 var…
Generalised gradients for virtual elements and applications to a posteriori error analysis
Théophile Chaumont-Frelet, Joscha Gedicke, Lorenzo Mascotto
We rewrite the standard nodal virtual element method as a generalised gradient method. This re-formulation allows for computing a reliable and efficient error estimator by locally…
The geometric error is less than the pollution error when solving the high-frequency Helmholtz equation with high-order FEM on curved domains
Théophile Chaumont-Frelet, Euan A. Spence
We consider the -version of the finite-element method, where accuracy is increased by decreasing the meshwidth while keeping the polynomial degree constant, applied to t…
An equilibrated estimator for mixed finite element discretizations of the curl-curl problem
T. Chaumont-Frelet
We propose a new a posteriori error estimator for mixed finite element discretizations of the curl-curl problem. This estimator relies on a Prager--Synge inequality, and therefore…
A hybridizable discontinuous Galerkin method with characteristic variables for Helmholtz problems
A. Modave, T. Chaumont-Frelet
A new hybridizable discontinuous Galerkin method, named the CHDG method, is proposed for solving time-harmonic scalar wave propagation problems. This method relies on a standard di…
A stable local commuting projector and optimal approximation estimates in
Théophile Chaumont-Frelet, Martin Vohralík
We design an operator from the infinite-dimensional Sobolev space to its finite-dimensional subspace formed by the Nédélec piecewise polynomials on…
Wavenumber-explicit stability and convergence analysis of hp finite element discretizations of Helmholtz problems in piecewise smooth media
M. Bernkopf, T. Chaumont-Frelet, J. M. Melenk
We present a wavenumber-explicit convergence analysis of the hp finite element method applied to a class of heterogeneous Helmholtz problems with piecewise analytic coefficients at…
Decay of coefficients and approximation rates in Gabor Gaussian frames
T. Chaumont-Frelet, M. Ingremeau
The aim of this note is to present a self-contained proof of the fact that a function can be approximated using a linear combination of Gaussian coherent states, with a number of t…
Bridging the Multiscale Hybrid-Mixed and Multiscale Hybrid High-Order methods
T. Chaumont-Frelet, A. Ern, S. Lemaire +1
We establish the equivalence between the Multiscale Hybrid-Mixed (MHM) and the Multiscale Hybrid High-Order (MsHHO) methods for a variable diffusion problem with piecewise polynomi…
On the derivation of guaranteed and p-robust a posteriori error estimates for the Helmholtz equation
T. Chaumont-Frelet, A. Ern, M. Vohralík
We propose a novel a posteriori error estimator for conforming finite element discretizations of two- and three-dimensional Helmholtz problems. The estimator is based on an equilib…
-robust equilibrated flux reconstruction in based on local minimizations. Application to a posteriori analysis of the curl-curl problem
Théophile Chaumont-Frelet, Martin Vohralík
We present a local construction of H(curl)-conforming piecewise polynomials satisfying a prescribed curl constraint. We start from a piecewise polynomial not contained in the H(cur…
Polynomial-degree-robust H(curl)-stability of discrete minimization in a tetrahedron
Théophile Chaumont-Frelet, Alexandre Ern, Martin Vohralík
We prove that the minimizer in the Nédélec polynomial space of some degree p > 0 of a discrete minimization problem performs as well as the continuous minimizer in H(curl), up to a…
Stable broken H(curl) polynomial extensions and p-robust a posteriori error estimates by broken patchwise equilibration for the curl-curl problem
Théophile Chaumont-Frelet, Alexandre Ern, Martin Vohralík
We study extensions of piecewise polynomial data prescribed in a patch of tetrahedra sharing an edge. We show stability in the sense that the minimizers over piecewise polynomial s…
A generalized finite element method for problems with sign-changing coefficients
Théophile Chaumont-Frelet, Barbara Verfürth
Problems with sign-changing coefficients occur, for instance, in the study of transmission problems with metamaterials. In this work, we present and analyze a generalized finite el…