Exploiting Superconvergence Through Smoothness-Increasing Accuracy-Conserving (SIAC) Filtering

Jennifer Ryan

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

3 Citations (Scopus)
3 Downloads (Pure)

Abstract

There has been much work in the area of superconvergent error analysis for finite element and discontinuous Galerkin (DG) methods. The property of superconvergence leads to the question of how to exploit this information in a useful manner, mainly through superconvergence extraction. There are many methods used for superconvergence extraction such as projection, interpolation, patch recovery and B-spline convolution filters. This last method falls under the class of Smoothness-Increasing Accuracy-Conserving (SIAC) filters. It has the advantage of improving both smoothness and accuracy of the approximation. Specifically, for linear hyperbolic equations it can improve the order of accuracy of a DG approximation from k + 1 to 2k + 1, where k is the highest degree polynomial used in the approximation, and can increase the smoothness to k − 1. In this article, we discuss the importance of overcoming the mathematical barriers in making superconvergence extraction techniques useful for applications, specifically focusing on SIAC filtering.
Original languageEnglish
Title of host publicationSpectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014
PublisherSpringer
Pages87-102
Volume105
ISBN (Print)978-3-319-19799-9
Publication statusPublished - 2015

Publication series

Name Lecture Notes in Computational Science and Engineering

Keywords

  • discontinuous Galerkin
  • hyperbolic equations
  • SIAC filtering
  • superconvergence
  • Post-processing

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