Smoothness-Increasing Accuracy-Conserving Filters for Discontinuous Galerkin Methods

Challenging the Assumptions of Symmetry and Uniformity

Doctoral thesis (2015)

Authors

X. Li Numerical Analysis -

Research Group

Numerical Analysis () (TU Delft)

Discontinuous Galerkin method Post-processing Superconvergence Nonuniform meshes SIAC filtering Boundaries

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Published Date

2015

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Numerical Analysis

Abstract

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 achieve a solution with higher accuracy order, reduced errors and improved smoothness.
The main contributions described in this dissertation are: 1) an efficient one-sided SIAC filter for both uniform and nonuniform meshes; 2) one-sided derivative SIAC filters for nonuniform meshes; 3) the theoretical and computational foundation for using SIAC filters for nonuniform meshes; and 4) the application of SIAC filters for streamline integration.