Jennifer Ryan
School of Mathematics, University of East Anglia, UK
Many numerical simulations produce data that contains hidden information. This hidden information can be exploited to create even more accurate representations of the data by appropriately constructing convolution post-processors. In this presentation we address one particular form of data - that of discontinuous Galerkin finite element methods. Specifically, a discussion how the Smoothness-Increasing Accuracy-Conserving (SIAC) post-processing filter takes advantage of the information hidden in the numerical solution and how to adapt the convolution kernel for boundaries, unstructured grids, and low-regularity solutions.
This presentation will focus on identifying where this hidden accuracy comes from, why the hidden accuracy is important, and how to construct convolution post-processors to take advantage of this information.