Numerical Analysis Seminar

Wednesday, August 27, 2008

Speaker: Jennifer K. Ryan , Assistant Professor
Delft Institute of Applied Mathematics
Delft University of Technology
Title: Local Smoothness-Increasing Accuracy-Conserving (SIAC) Post-Processing for discontinuous Galerkin methods
Time: 3:00-4:00 pm
Place: Blocker 627

Abstract

The discontinuous Galerkin (DG) method continues to be a popular method due to several nice features including flexibility for adaptivity and for the ability to maintain high order approximations when discontinuities occur at inter-element boundaries. There have been previous investigations into post-processing of discontinuous Galerkin solutions for linear hyperbolic equations by Cockburn, Luskin, Shu, and Suli based on the work of Bramble and Schatz as well as Mock and Lax. This post-processing technique relies on negative order norm estimates of the numerical solution and is able to improve the order of accuracy for time-dependent linear hyperbolic partial differential equations from order k+1 to order 2k+1 while filtering out oscillations in the error over a uniform quadrilateral mesh.

In this talk I will discuss this post-processing technique and give examples that demonstrate the ability of the post-processor to enhance discontinuous Galerkin solutions. Extensions of this technique to one-sided post-processing as well as two techniques for extending the applications to smoothly varying and non-uniform mesh structures will also be presented. Additionally, this post-processing technique has recently shown to be a promising tool for filtering DG solutions to allow for visualization of streamlines. As part of this application, a discussion on the possibility of using this technique for one-dimensional filtering of multi-dimensional data to aid in calculation of streamlines will be given.

Last revised: 08/26/08 By: abnersg@math