Smoothness-Increasing Accuracy-Conserving (SIAC) Filtering for Discontinuous Galerkin Solutions over Nonuniform Meshes: Superconvergence and Optimal Accuracy

Smoothness-increasing accuracy-conserving (SIAC) filtering is an area of increasing interest because it can extract the “hidden accuracy” in discontinuous Galerkin (DG) solutions. It has been shown that by applying a SIAC filter to a DG solution, the accuracy order of the DG solution improves from order k+ 1 to order 2 k+ 1 for linear...

Automated Parameters for Troubled-Cell Indicators Using Outlier Detection

In Vuik and Ryan [J. Comput. Phys., 270 (2014), pp. 138--160] we studied the use of troubled-cell indicators for discontinuity detection in nonlinear hyperbolic partial differential equations and introduced a new multiwavelet technique to detect troubled cells. We found that these methods perform well as long as a suitable, problem-dependent...

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...