Optimal penalty parameters for symmetric discontinuous Galerkin discretisations of the time-harmonic Maxwell equations

D. Sarmany, F. Izsak, Jacobus J.W. van der Vegt

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    Abstract

    We provide optimal parameter estimates and a priori error bounds for symmetric discontinuous Galerkin (DG) discretisations of the second-order indefinite time-harmonic Maxwell equations. More specifically, we consider two variations of symmetric DG methods: the interior penalty DG (IP-DG) method and one that makes use of the local lifting operator in the flux formulation. As a novelty, our parameter estimates and error bounds are (i) valid in the pre-asymptotic regime; (ii) solely depend on the geometry and the polynomial order; and (iii) are free of unspecified constants. Such estimates are particularly important in three-dimensional (3D) simulations because in practice many 3D computations occur in the pre-asymptotic regime. Therefore, it is vital that our numerical experiments that accompany the theoretical results are also in 3D. They are carried out on tetrahedral meshes with high-order (p = 1, 2, 3, 4) hierarchic H(curl)-conforming polynomial basis functions.
    Original languageUndefined
    Pages (from-to)219-254
    Number of pages36
    JournalJournal of scientific computing
    Volume44
    Issue number3
    DOIs
    Publication statusPublished - 2010

    Keywords

    • EWI-18631
    • MSC-00A72
    • IR-73800
    • Electromagnetic waves
    • METIS-271085
    • Numerical approximation

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