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23 papers · 1 filter
Optimal convergence rates of an adaptive finite element method for unbounded domains
Théophile Chaumont-Frelet, Gregor Gantner
We consider linear reaction-diffusion equations posed on unbounded domains, and discretized by adaptive Lagrange finite elements. To obtain finite-dimensional spaces, it is necessa…
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 …
Finite Volumes for a dissipative free boundary problem
Clément Cancès, Claire Chainais-Hillairet, Amélie Dupouy
We study a toy model for the evolution of the oxygen concentration in an oxide layer. It consists in a transient convection diffusion equation in a one-dimensional domain of variab…
A posteriori error estimates and space-adaptive mesh refinements for time-dependent scattering problems
Théophile Chaumont-Frelet, Heiko Gimperlein, Ignacio Labarca-Figueroa +1
This work studies a posteriori error estimates and their use for time-dependent acoustic scattering problems, formulated as a time-dependent boundary integral equation based on a s…
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 quasi-interpolation operator yielding fully computable error bounds
T. Chaumont-Frelet, M. Vohralik
We design a quasi-interpolation operator from the Sobolev space to its finite-dimensional finite element subspace formed by piecewise polynomials on a simplicial mesh wi…