The interpolation of differential forms is a challenging problem that is getting increasing attention. The issue of finding unisolvent degrees of freedom to describe a differential form in terms of high-order Whitney forms is an active area of research nowadays. In this paper we deal with a family of such degrees of freedom, called weights, that fits with the physical and geometrical nature of the field to interpolate. These weights play the role of interpolation coefficients when reconstructing scalar/vector fields in terms of a set of selected multivariate polynomial forms. Weights are a generalization of the evaluations of a scalar function at a set of nodes in view of its reconstruction on multivariate polynomial bases. As in the nodal case, different sets of such weights are compared in terms of a Lebesgue constant. In this contribution, we briefly recall their definition and provide examples of algorithms in low dimension to compute their associated Lebesgue constant value. Insights to greater dimensions are offered as well.

Computing weights for high order Whitney edge elements* / Bruni Bruno, L.; Alonso Rodriguez, A.; Rapetti, F.. - In: DOLOMITES RESEARCH NOTES ON APPROXIMATION. - ISSN 2035-6803. - 15:2(2022), pp. 1-12. [10.14658/pupj-drna-2022-2-1]

Computing weights for high order Whitney edge elements*

Bruni Bruno L.;Alonso Rodriguez A.;Rapetti F.
2022-01-01

Abstract

The interpolation of differential forms is a challenging problem that is getting increasing attention. The issue of finding unisolvent degrees of freedom to describe a differential form in terms of high-order Whitney forms is an active area of research nowadays. In this paper we deal with a family of such degrees of freedom, called weights, that fits with the physical and geometrical nature of the field to interpolate. These weights play the role of interpolation coefficients when reconstructing scalar/vector fields in terms of a set of selected multivariate polynomial forms. Weights are a generalization of the evaluations of a scalar function at a set of nodes in view of its reconstruction on multivariate polynomial bases. As in the nodal case, different sets of such weights are compared in terms of a Lebesgue constant. In this contribution, we briefly recall their definition and provide examples of algorithms in low dimension to compute their associated Lebesgue constant value. Insights to greater dimensions are offered as well.
2022
2
Bruni Bruno, L.; Alonso Rodriguez, A.; Rapetti, F.
Computing weights for high order Whitney edge elements* / Bruni Bruno, L.; Alonso Rodriguez, A.; Rapetti, F.. - In: DOLOMITES RESEARCH NOTES ON APPROXIMATION. - ISSN 2035-6803. - 15:2(2022), pp. 1-12. [10.14658/pupj-drna-2022-2-1]
File in questo prodotto:
File Dimensione Formato  
01_DRNA_SA2022_0.pdf

accesso aperto

Tipologia: Versione editoriale (Publisher’s layout)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 279.17 kB
Formato Adobe PDF
279.17 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/360867
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 2
social impact