Algebraic Dual Polynomials for the Equivalence of Curl-Curl Problems

Conference paper (2020)

Authors

M.I. Gerritsma Aerodynamics - Aerospace Engineering

V. Jain Aerodynamics - Aerospace Engineering

Y. Zhang Aerodynamics - Aerospace Engineering

A. Palha Eindhoven University of Technology

Research Group

Aerodynamics (Aerospace Engineering) (TU Delft)

Spectral element method Algebraic dual polynomials Curl-curl problems

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Published Date

2020

Language

English

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Faculty

Aerospace Engineering

Department

Flow Physics and Technology

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.