cite as

.bib

@InProceedings{Zhang2020Discrete,
    author="Zhang, Yi
    and Jain, Varun
    and Palha, Artur
    and Gerritsma, Marc",
    editor="Sherwin, Spencer J.
    and Moxey, David
    and Peir{\'o}, Joaquim
    and Vincent, Peter E.
    and Schwab, Christoph",
    title="Discrete Equivalence of Adjoint Neumann--Dirichlet div-grad and grad-div Equations in Curvilinear 3D Domains",
    booktitle="Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018",
    year="2020",
    publisher="Springer International Publishing",
    address="Cham",
    pages="203--213",
    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.",
    isbn="978-3-030-39647-3"
}

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