Multiwavelets and Jumps in DG Approximations

Mathea Vuik, Jennifer Ryan

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    6 Citations (Scopus)

    Abstract

    In general, solutions of nonlinear hyperbolic PDEs contain shocks or develop discontinuities. One option for improving the numerical treatment of the spurious oscillations that occur near these artifacts is through the application of a limiter. The cells where such treatment is necessary are referred to as troubled cells. In this article, we discuss the multiwavelet troubled-cell indicator that was introduced by Vuik and Ryan (J Comput Phys 270:138–160, 2014). We focus on the relation between the highest-level multiwavelet coefficients and jumps in (derivatives of) the DG approximation. Based on this information, we slightly modify the original multiwavelet troubled-cell indicator. Furthermore, we show one-dimensional test cases using the modified multiwavelet troubled-cell indicator.
    Original languageEnglish
    Title of host publicationSpectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014
    PublisherSpringer
    Pages503-511
    Number of pages9
    Volume106
    ISBN (Electronic)978-3-319-19800-2
    ISBN (Print)978-3-319-19799-9
    Publication statusPublished - Dec 2015

    Publication series

    NameLecture Notes in Computational Science and Engineering
    PublisherSpringer

    Keywords

    • discontinuous Galerkin
    • multi-wavelets
    • hyperbolic equations
    • discontinuity detection

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