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

Ryan, Jennifer (2015) Exploiting Superconvergence Through Smoothness-Increasing Accuracy-Conserving (SIAC) Filtering. In: Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014. Lecture Notes in Computational Science and Engineering, 105 . Springer, pp. 87-102. ISBN 978-3-319-19799-9

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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.

Item Type: Book Section
Uncontrolled Keywords: discontinuous galerkin,hyperbolic equations,siac filtering,superconvergence,post-processing
Faculty \ School: Faculty of Science > School of Mathematics
Depositing User: Pure Connector
Date Deposited: 05 Feb 2016 14:01
Last Modified: 15 Aug 2020 00:01
URI: https://ueaeprints.uea.ac.uk/id/eprint/56973
DOI:

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