Towards nonuniform distributions of unisolvent weights for high-order Whitney edge elements
Résumé
We propose to extend results on the interpolation theory for scalar functions to
the case of differential k-forms. More precisely, we consider the interpolation of
fields in the finite element spaces of trimmed polynomial k-forms of
arbitrary degree r ≥ 1, from their weights, namely their integrals on k-chains.
These integrals have a clear physical interpretation, such as circulations along
curves, fluxes across surfaces, densities in volumes, depending on the value of
k. In this work, for k = 1, we rely on the flexibility of the weights with respect
to their geometrical support, to study different sets of 1-chains in T for a high
order interpolation of differential 1-forms, constructed starting from “good” sets
of nodes for a high order multi-variate polynomial representation of scalar fields,
namely 0-forms. We analyse the growth of the generalized Lebesgue constant
with the degree r and preliminary numerical results for edge elements support
the nonuniform choice, in agreement with the well-known nodal case.
Domaines
Analyse numérique [math.NA]
Origine : Fichiers produits par l'(les) auteur(s)