Algebraic Dual Polynomials for the Equivalence of Curl-Curl Problems

  • Marc GerritsmaEmail author
  • Varun Jain
  • Yi Zhang
  • Artur Palha
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 132)


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 \(\boldsymbol {n} \times \boldsymbol {E} = \hat {E}_{\dashv }\) on E and Neumann boundary conditions \(\boldsymbol {n} \times \mathbf {{curl}}\,F=\hat {E}_{\dashv }\), 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.


Spectral element method Algebraic dual polynomials Curl-curl problems 


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Marc Gerritsma
    • 1
    Email author
  • Varun Jain
    • 1
  • Yi Zhang
    • 1
  • Artur Palha
    • 2
  1. 1.Faculty of Aerospace EngineeringTU DelftDelftThe Netherlands
  2. 2.Department of Mechanical EngineeringEindhoven University of TechnologyEindhovenThe Netherlands

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