An exterior calculus framework for polytopal methods
We develop in this work the first polytopal complexes of differential forms. These complexes,
inspired by the Discrete De Rham and the Virtual Element approaches, are discrete versions …
inspired by the Discrete De Rham and the Virtual Element approaches, are discrete versions …
A discrete Weber inequality on three-dimensional hybrid spaces with application to the HHO approximation of magnetostatics
We prove a discrete version of the first Weber inequality on three-dimensional hybrid spaces
spanned by vectors of polynomials attached to the elements and faces of a polyhedral mesh …
spanned by vectors of polynomials attached to the elements and faces of a polyhedral mesh …
Local finite element approximation of Sobolev differential forms
We address fundamental aspects in the approximation theory of vector-valued finite element
methods, using finite element exterior calculus as a unifying framework. We generalize the …
methods, using finite element exterior calculus as a unifying framework. We generalize the …
Discrete Weber inequalities and related Maxwell compactness for hybrid spaces over polyhedral partitions of domains with general topology
S Lemaire, S Pitassi - Foundations of Computational Mathematics, 2024 - Springer
We prove discrete versions of the first and second Weber inequalities on H (curl)∩ H (div η)-
like hybrid spaces spanned by polynomials attached to the faces and to the cells of a …
like hybrid spaces spanned by polynomials attached to the faces and to the cells of a …
[HTML][HTML] Uniform Poincaré inequalities for the Discrete de Rham complex on general domains
DA Di Pietro, ML Hanot - Results in Applied Mathematics, 2024 - Elsevier
In this paper we prove Poincaré inequalities for the Discrete de Rham (DDR) sequence on a
general connected polyhedral domain Ω of R 3. We unify the ideas behind the inequalities …
general connected polyhedral domain Ω of R 3. We unify the ideas behind the inequalities …
Higher-order finite element de Rham complexes, partially localized flux reconstructions, and applications
MW Licht - arXiv preprint arXiv:2310.10479, 2023 - arxiv.org
We construct finite element de~ Rham complexes of higher and possibly non-uniform
polynomial order in finite element exterior calculus (FEEC). Starting from the finite element …
polynomial order in finite element exterior calculus (FEEC). Starting from the finite element …