Smoothness-Increasing Accuracy-Conserving Filters for Discontinuous Galerkin Methods: Challenging the Assumptions of Symmetry and Uniformity

In this dissertation, we focus on exploiting superconvergence for discontinuous Galerkin methods and constructing a superconvergence extraction technique, in particular, Smoothness-Increasing Accuracy-Conserving (SIAC) filtering. The SIAC filtering technique is based on the superconvergence property of discontinuous Galerkin methods and aims to...