Sharp Penalty Term and Time Step Bounds for the Interior Penalty Discontinuous Galerkin Method for Linear Hyperbolic Problems

Sjoerd Geevers, J.J.W. van der Vegt

    Research output: Contribution to journalArticleAcademicpeer-review

    17 Downloads (Pure)

    Abstract

    We present sharp and sucient bounds for the interior penalty term and time step size to ensure stability of the symmetric interior penalty discontinuous Galerkin (SIPDG) method combined with an explicit time-stepping scheme. These conditions hold for generic meshes, including unstructured nonconforming heterogeneous meshes of mixed element types, and apply to a large class of linear hyperbolic problems, including the acoustic wave equation, the (an)isotropic elastic wave equations, and Maxwell's equations. The penalty term bounds are computed elementwise, while bounds for the time step size are computed at weighted submeshes requiring only a small number of elements and faces. Numerical results illustrate the sharpness of these bounds.
    Original languageEnglish
    Pages (from-to)A1851-A1878
    Number of pages27
    JournalSIAM journal on scientific computing
    Volume39
    Issue number5
    DOIs
    Publication statusPublished - 6 Sep 2017

    Keywords

    • Stability analysis
    • Time step estimate
    • Penalty term estimate
    • Interior penalty method
    • Discontinuous Galerkin method
    • Linear wave problems

    Fingerprint

    Dive into the research topics of 'Sharp Penalty Term and Time Step Bounds for the Interior Penalty Discontinuous Galerkin Method for Linear Hyperbolic Problems'. Together they form a unique fingerprint.

    Cite this