Projects per year
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.
|Title of host publication||Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014|
|Number of pages||16|
|Publication status||Published - 2015|
|Name||Lecture Notes in Computational Science and Engineering|
- discontinuous Galerkin
- hyperbolic equations
- SIAC filtering
- 1 Finished
- 5 Citations (Scopus)
- 1 Article
Divided difference estimates and accuracy enhancement of discontinuous Galerkin methods for nonlinear symmetric systems of hyperbolic conservation lawsMeng, X. & Ryan, J. K., 25 Jan 2018, In: IMA Journal of Numerical Analysis. 38, 1, p. 125–155 31 p.
Research output: Contribution to journal › Article › peer-reviewOpen AccessFile8 Citations (Scopus)13 Downloads (Pure)