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Dispersive properties of high order nedelec/edge element approximation of the time-harmonic Maxwell equations

Ainsworth, Mark (2004) Dispersive properties of high order nedelec/edge element approximation of the time-harmonic Maxwell equations. Philosophical Transactions A: Mathematical, Physical and Engineering Sciences, 362 (1816). pp. 471-493. ISSN 1364-503X

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    Abstract

    The dispersive behaviour of high-order Næ#169;dæ#169;lec element approximation of the time harmonic Maxwell equations at a prescribed temporal frequency ω on tensor-product meshes of size h is analysed. A simple argument is presented, showing that the discrete dispersion relation may be expressed in terms of that for the approximation of the scalar Helmholtz equation in one dimension. An explicit form for the one-dimensional dispersion relation is given, valid for arbitrary order of approximation. Explicit expressions for the leading term in the error in the regimes where ωh is small, showing that the dispersion relation is accurate to order 2p for a pth-order method; and in the high-wavenumber limit where 1«ωh, showing that in this case the error reduces at a super-exponential rate once the order of approximation exceeds a certain threshold, which is given explicitly.

    Item type: Article
    ID code: 64
    Keywords: edge finite element, numerical dispersion, discrete dispersion relation, Mathematics, Physics
    Subjects: Science > Mathematics
    Science > Physics
    Department: Faculty of Science > Mathematics and Statistics
    Related URLs:
    Depositing user: Mr Derek Boyle
    Date Deposited: 21 Dec 2005
    Last modified: 20 Aug 2012 17:43
    URI: http://strathprints.strath.ac.uk/id/eprint/64

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