cite as

.bib

@Inbook{Gerritsma2020Algebraic,
    author="Gerritsma, Marc
    and Jain, Varun
    and Zhang, Yi
    and Palha, Artur",
    editor="van Brummelen, Harald
    and Corsini, Alessandro
    and Perotto, Simona
    and Rozza, Gianluigi",
    title="Algebraic Dual Polynomials for the Equivalence of Curl-Curl Problems",
    bookTitle="Numerical Methods for Flows: FEF 2017 Selected Contributions",
    year="2020",
    publisher="Springer International Publishing",
    address="Cham",
    pages="307--320",
    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{\texttimes}E={\^E}⊣{\$}{\$}{\backslash}boldsymbol {\{}n{\}} {\backslash}times {\backslash}boldsymbol {\{}E{\}} = {\backslash}hat {\{}E{\}}{\_}{\{}{\backslash}dashv {\}}{\$}{\$}on E and Neumann boundary conditions n{\texttimes}curlF={\^E}⊣{\$}{\$}{\backslash}boldsymbol {\{}n{\}} {\backslash}times {\backslash}mathbf {\{}{\{}curl{\}}{\}}{\backslash},F={\backslash}hat {\{}E{\}}{\_}{\{}{\backslash}dashv {\}}{\$}{\$}, we expect the solutions to satisfy E{\thinspace}={\thinspace}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.",
    isbn="978-3-030-30705-9",
    doi="10.1007/978-3-030-30705-9_27",
    url="https://doi.org/10.1007/978-3-030-30705-9_27"
}

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