Smoothness-Increasing Accuracy-Conserving (SIAC) Filters in Fourier Space

Liangyue Ji, Jennifer Ryan

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

4 Citations (Scopus)


It has been noted in the past that discontinuous Galerkin methods can be viewed as a low order multi-domain Spectral method with penalty term (Hesthaven et al., Spectral methods for time-dependent problems, Cambridge University Press, Cambridge, 2007). It is then logical to first ask how to relate filters in Spectral Methods to Smoothness-Increasing Accuracy-Conservin (SIAC) filters, which are typically applied to approximations obtained via the discontinuous Galerkin methods. In this article we make a first effort to relate Smoothness-Increasing Accuracy-Conserving filtering to filtering for Spectral Methods. We frame this discussion in the context of Vandeven (J Sci Comput 6:159–192, 1991).
Original languageEnglish
Title of host publicationSpectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014
Number of pages9
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


  • discontinuous Galerkin
  • SIAC filtering
  • Spectral methods
  • filtering

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