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The Discrete Relations Between Fields and Potentials with High Order Whitney Forms

  • Ana M. Alonso RodríguezEmail author
  • Francesca Rapetti
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 126)

Abstract

When using the lower order Whitney elements on a simplicial complex, the matrices describing the external derivative, namely, the differential operators gradient, curl and divergence, are the incidence matrices between edges and vertices, faces and edges, tetrahedra and faces. For higher order Whitney elements, if one adopts degrees of freedom based on moments, the entries of these matrices are still equal to 0, 1 or − 1 but they are no more incidence matrices. If one uses instead the “weights of the field on small simplices” as alternative degrees of freedom, the matrices representative of the external derivative are incidence matrices for any polynomial degree.

Notes

Acknowledgements

Ana Alonso Rodríguez thanks the Laboratoire de Mathématiques J.A. Dieudonné, Université Côte d’Azur, Nice, France, where this work started.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Dip. di Matematica, Università degli Studi di TrentoPovo, TrentoItaly
  2. 2.Dep. de Mathématiques J.-A. Dieudonné, Univ. Côte d’AzurNiceFrance

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