Algebraic Dual Polynomials for the Equivalence of Curl-Curl Problems

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Abstract

In this paper we will consider two curl-curl equations in two dimensions. One curl-curl problem for a scalar quantity F and one problem for a vector field E. For Dirichlet boundary conditions n× E= Ê on E and Neumann boundary conditions n×curlF=Ê⊣, we expect the solutions to satisfy E = curl F. When we use algebraic dual polynomial representations, these identities continue to hold at the discrete level. Equivalence will be proved and illustrated with a computational example.

Original languageEnglish
Title of host publicationNumerical Methods for Flows - FEF 2017 Selected Contributions
EditorsHarald van Brummelen, Alessandro Corsini, Simona Perotto, Gianluigi Rozza
PublisherSpringer Open
Pages307-320
Number of pages14
ISBN (Print)9783030307042
DOIs
Publication statusPublished - 2020
Event19th International Conference on Finite Elements in Flow Problems, FEF 2017 - Rome, Italy
Duration: 5 Apr 20177 Apr 2017

Publication series

NameLecture Notes in Computational Science and Engineering
Volume132
ISSN (Print)1439-7358
ISSN (Electronic)2197-7100

Conference

Conference19th International Conference on Finite Elements in Flow Problems, FEF 2017
CountryItaly
CityRome
Period5/04/177/04/17

Keywords

  • Algebraic dual polynomials
  • Curl-curl problems
  • Spectral element method

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