Algebraic Dual Polynomials for the Equivalence of Curl-Curl Problems

Gerritsma, MI; Jain, V.; Zhang, Yi; Palha da Silva Clérigo, A.

Algebraic Dual Polynomials for the Equivalence of Curl-Curl Problems

Conference paper (2020)

Authors

MI Gerritsma Aerodynamics

V. Jain Aerodynamics

Yi Zhang Aerodynamics

A. Palha da Silva Clérigo Eindhoven University of Technology

Research Group

Aerodynamics

Spectral element method Algebraic dual polynomials Curl-curl problems

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Published Date

2020

Language

English

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Research Group

Aerodynamics

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.

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