Abstract
AbstractWe 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 $${\mathcal P}^-_r \varLambda ^k(T)$$
P
r
-
Λ
k
(
T
)
, the finite element spaces of trimmed polynomial k-forms of arbitrary degree $$r \ge 1$$
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 $$k=1$$
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.
Funder
Ministero dell’Istruzione, dell’Università e della Ricerca
Institut National des Sciences de l’Univers, Centre National de la Recherche Scientifique
Università degli Studi di Trento
Publisher
Springer Science and Business Media LLC
Subject
Computational Mathematics,Algebra and Number Theory
Cited by
2 articles.
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