Smoothness-Increasing Accuracy-Conserving Filters for Discontinuous Galerkin Solutions over Unstructured Triangular Meshes

The discontinuous Galerkin (DG) method has very quickly found utility in such diverse applications as computational solid mechanics, fluid mechanics, acoustics, and electromagnetics. The DG methodology merely requires weak constraints on the fluxes between elements. This feature provides a flexibility which is difficult to match with...

Smoothness-Increasing Accuracy-Conserving (SIAC) Postprocessing for Discontinuous Galerkin Solutions over Structured Triangular Meshes

Theoretically and computationally, it is possible to demonstrate that the order of accuracy of a discontinuous Galerkin (DG) solution for linear hyperbolic equations can be improved from order $k$+1 to 2$k$+1 through the use of smoothness-increasing accuracy-conserving (SIAC) filtering. However, it is a computationally complex task to perform...

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

The discontinuous Galerkin (DG) methods provide a high-order extension of the finite volume method in much the same way as high-order or spectral/hp elements extend standard finite elements. However, lack of inter-element continuity is often contrary to the smoothness assumptions upon which many post-processing algorithms such as those used in...

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

The discontinuous Galerkin (DG) method continues to maintain heightened levels of interest within the simulation community because of the discretization flexibility it provides. Although one of the fundamental properties of the DG methodology and arguably its most powerful property is the ability to combine high-order discretizations on an...