Discrete equivalence of adjoint neumann–dirichlet div-grad and grad-div equations in curvilinear 3d domains

Zhang, Yi; Jain, V.; Palha da Silva Clerigo, A; Gerritsma, M.

doi:10.1007/978-3-030-39647-3_15

Discrete equivalence of adjoint neumann–dirichlet div-grad and grad-div equations in curvilinear 3d domains

Conference paper (2020)

Authors

Yi Zhang Student

V. Jain Aerodynamics

A Palha da Silva Clerigo Eindhoven University of Technology

M. Gerritsma Aerodynamics

Research Group

Aerodynamics

DOI: https://doi.org/10.1007/978-3-030-39647-3_15

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Published Date

2020

Language

English

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Research Group

Aerodynamics

Abstract

In this paper, we will show that the equivalence of a div-grad Neumann problem and a grad-div Dirichlet problem can be preserved at the discrete level in 3-dimensional curvilinear domains if algebraic dual polynomial representations are employed. These representations will be introduced. Proof of the equivalence at the discrete level follows from the construction of the algebraic dual representations. A 3-dimensional test problem in curvilinear coordinates will illustrate this approach.

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