Smoothness-Increasing Accuracy-Conserving (SIAC) Filtering for Discontinuous Galerkin Solutions: Improved Errors Versus Higher-Order Accuracy

Smoothness-increasing accuracy-conserving (SIAC) filtering has demonstrated its effectiveness in raising the convergence rate of discontinuous Galerkin solutions from order k + 12 to order 2k + 1 for specific types of translation invariant meshes (Cockburn et al. in Math. Comput. 72:577–606, 2003; Curtis et al. in SIAM J. Sci. Comput. 30(1):272...

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...

Position-dependent smoothness-increasing accuracy-conserving (SIAC) filtering for improving discontinuous Galerkin solutions

Position-dependent smoothness-increasing accuracy-conserving (SIAC) filtering is a promising technique not only in improving the order of the numerical solution obtained by a discontinuous Galerkin (DG) method but also in increasing the smoothness of the field and improving the magnitude of the errors. This was initially established as an...