Fourier Continuation Discontinuous Galerkin Methods for Linear Hyperbolic Problems

04/30/2021 ∙ by Daniel Appelo, et al. ∙ 0

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.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 18

This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.