Projects per year
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 Bspline convolution filters. This last method falls under the class of SmoothnessIncreasing AccuracyConserving (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 language  English 

Title of host publication  Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014 
Publisher  Springer 
Pages  87102 
Volume  105 
ISBN (Print)  9783319197999 
Publication status  Published  2015 
Publication series
Name  Lecture Notes in Computational Science and Engineering 

Keywords
 discontinuous Galerkin
 hyperbolic equations
 SIAC filtering
 superconvergence
 Postprocessing
Projects
 1 Finished

Exploiting Superconvergence in Discontinuous Galerkin Methods for Improved TimeStepping and Visualization
Ryan, J.
1/02/13 → 31/07/16
Project: Research
Research output
 4 Citations (Scopus)
 1 Article

Divided difference estimates and accuracy enhancement of discontinuous Galerkin methods for nonlinear symmetric systems of hyperbolic conservation laws
Meng, X. & Ryan, J. K., 25 Jan 2018, In: IMA Journal of Numerical Analysis. 38, 1, p. 125–155Research output: Contribution to journal › Article › peerreview
Open AccessFile6 Citations (Scopus)9 Downloads (Pure)