Fourier Continuation Discontinuous Galerkin Methods for Linear Hyperbolic Problems
Numerical Analysis
2021-05-04 v1 Numerical Analysis
Abstract
Fourier continuation is an approach used to create periodic extensions of non-periodic functions in order to obtain highly-accurate Fourier expansions. These methods have been used in PDE-solvers and have demonstrated high-order convergence and spectrally accurate dispersion relations in numerical experiments. Discontinuous Galerkin (DG) methods are increasingly used for solving PDEs and, as all Galerkin formulations, come with a strong framework for proving stability and convergence. Here we propose the use of Fourier continuation in forming a new basis for the DG framework.
Cite
@article{arxiv.2105.00123,
title = {Fourier Continuation Discontinuous Galerkin Methods for Linear Hyperbolic Problems},
author = {Daniel Appelo and Kiera van der Sande and Nathan Albin},
journal= {arXiv preprint arXiv:2105.00123},
year = {2021}
}