Multiwavelets and Jumps in DG Approximations

Mathea J. Vuik*, Jennifer K. Ryan

*Corresponding author for this work

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

5 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 originalmultiwavelet troubled-cell indicator. Furthermore, we show onedimensional 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
Subtitle of host publicationSelected papers from the ICOSAHOM Conference
EditorsRobert M. Kirby, Martin Berzins, Jan S. Hesthaven
Place of PublicationCham
PublisherSpringer
Pages503-511
Number of pages9
ISBN (Electronic)978-3-319-19800-2
ISBN (Print)978-3-319-19799-9
DOIs
Publication statusPublished - 2015
EventICOSAHOM 2014: International Conference on Spectral and High-Order Methods - Salt Lake City, UT, United States
Duration: 23 Jun 201427 Jun 2014

Publication series

NameLecture Notes in Computational Science and Engineering
Volume106
ISSN (Print)1439-7358

Conference

ConferenceICOSAHOM 2014
Country/TerritoryUnited States
CitySalt Lake City, UT
Period23/06/1427/06/14

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