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2021 | OriginalPaper | Chapter

High Order Whitney Forms on Simplices and the Question of Potentials

Authors : Francesca Rapetti, Ana Alonso Rodríguez

Published in: Numerical Mathematics and Advanced Applications ENUMATH 2019

Publisher: Springer International Publishing

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Abstract

In the frame of high order finite element approximations of PDEs, we are interested in an explicit and efficient way for constructing finite element functions with assigned gradient, curl or divergence in domains with general topology. Three ingredients, that bear the name of their scientific fathers, are involved: the de Rham’s diagram and theorem, Hodge’s decomposition for vectors, Whitney’s differential forms. Some key images are presented in order to illustrate the mathematical concepts.

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next chapter The Candy Wrapper Problem: A Temporal Multiscale Approach for PDE/PDE Systems
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Metadata
Title
High Order Whitney Forms on Simplices and the Question of Potentials
Authors
Francesca Rapetti
Ana Alonso Rodríguez
Copyright Year
2021
Book
Numerical Mathematics and Advanced Applications ENUMATH 2019

Print ISBN: 978-3-030-55873-4

Electronic ISBN: 978-3-030-55874-1

Copyright Year: 2021

DOI
https://doi.org/10.1007/978-3-030-55874-1_1

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