Extension of a Post Processing Technique for the Discontinuous Galerkin Method for Hyperbolic Equations with Application to an Aeroacoustic Problem

Authors:
Jennifer Ryan;Chi-Wang Shu;Harold Atkins
Affiliations:
-;-;-
Venue:
SIAM Journal on Scientific Computing
Year:
2005

Citing 0
Cited 13

Locally divergence-free discontinuous Galerkin methods for the Maxwell equations

Journal of Computational Physics
A unified framework for the construction of one-step finite volume and discontinuous Galerkin schemes on unstructured meshes

Journal of Computational Physics
One-Sided Smoothness-Increasing Accuracy-Conserving Filtering for Enhanced Streamline Integration through Discontinuous Fields

Journal of Scientific Computing
Local derivative post-processing for the discontinuous Galerkin method

Journal of Computational Physics
Quantification of Errors Introduced in the Numerical Approximation and Implementation of Smoothness-Increasing Accuracy Conserving (SIAC) Filtering of Discontinuous Galerkin (DG) Fields

Journal of Scientific Computing
Position-Dependent Smoothness-Increasing Accuracy-Conserving (SIAC) Filtering for Improving Discontinuous Galerkin Solutions

SIAM Journal on Scientific Computing
Smoothness-Increasing Accuracy-Conserving (SIAC) Postprocessing for Discontinuous Galerkin Solutions over Structured Triangular Meshes

SIAM Journal on Numerical Analysis
Superconvergence of Discontinuous Galerkin Solutions for Delay Differential Equations of Pantograph Type

SIAM Journal on Scientific Computing
On the Negative-Order Norm Accuracy of a Local-Structure-Preserving LDG Method

Journal of Scientific Computing
Efficient Implementation of Smoothness-Increasing Accuracy-Conserving (SIAC) Filters for Discontinuous Galerkin Solutions

Journal of Scientific Computing
Superconvergence of discontinuous Galerkin and local discontinuous Galerkin methods: Eigen-structure analysis based on Fourier approach

Journal of Computational Physics
A scalable, efficient scheme for evaluation of stencil computations over unstructured meshes

SC '13 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
Smoothness-Increasing Accuracy-Conserving (SIAC) Filters for Discontinuous Galerkin Solutions: Application to Structured Tetrahedral Meshes

Journal of Scientific Computing

Quantified Score

Hi-index	0.02

Visualization

Abstract

In this paper we further explore a local postprocessing technique, originally developed by Bramble and Schatz [Math. Comp., 31 (1977), pp. 94--111] using continuous finite element methods for elliptic problems and later by Cockburn et al. [Math. Comp., 72 (2003), pp. 577--606] using discontinuous Galerkin methods for hyperbolic equations. We investigate the technique in the context of superconvergence of the derivatives of the numerical solution, two space dimensions for both tensor product local basis and the usual kth degree polynomials basis, multidomain problems with different mesh sizes, variable coefficient linear problems including those with discontinuous coefficients, and linearized Euler equations applied to an aeroacoustic problem. We demonstrate through extensive numerical examples that the technique is very effective in all these situations in enhancing the accuracy of the discontinuous Galerkin solutions.