Time-integration methods for finite element discretisations of the second-order Maxwell equation

D. Sarmany, Mikhail A. Bochev, Jacobus J.W. van der Vegt

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    Abstract

    This article deals with time integration for the second-order Maxwell equations with possibly non-zero conductivity in the context of the discontinuous Galerkin finite element method (DG-FEM) and the H(curl)-conforming FEM. For the spatial discretisation, hierarchic H(curl)-conforming basis functions are used up to polynomial order p = 3 over tetrahedral meshes, meaning fourth-order convergence rate. A high-order polynomial basis often warrants the use of high-order time-integration schemes, but many well-known high-order schemes may suffer from a severe time-step stability restriction owing to the conductivity term. We investigate several possible time-integration methods from the point of view of accuracy, stability and computational work. We also carry out a numerical Fourier analysis to study the dispersion and dissipation properties of the semi-discrete DG-FEM scheme as well as the fully-discrete schemes with several of the time-integration methods. The dispersion and dissipation properties of the spatial discretisation and those of the time-integration methods are investigated separately, providing additional insight into the two discretisation steps.
    Original languageUndefined
    Pages (from-to)528-543
    Number of pages16
    JournalComputers and mathematics with applications
    Volume65
    Issue number3
    DOIs
    Publication statusPublished - Feb 2013

    Keywords

    • EWI-23229
    • Discontinuous Galerkin finite element method
    • H(curl)-conforming finite element method
    • IR-85338
    • Second-order damped Maxwell wave equation
    • METIS-296382
    • High-order numerical time integration

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