Fourier Continuation Discontinuous Galerkin Methods for Linear Hyperbolic Problems

被引：0
作者：
Kiera van der Sande
Daniel Appelö
Nathan Albin
机构：
[1] University of Colorado Boulder,Department of Applied Mathematics
[2] Michigan State University,Department of Computational Mathematics, Science & Engineering
[3] Michigan State University,Department of Mathematics
[4] Kansas State University,Department of Mathematics
来源：
Communications on Applied Mathematics and Computation | 2023年 / 5卷
关键词：
Discontinuous Galerkin; Fourier continuation (FC); High order method; 65M60; 65M06;
D O I：
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中图分类号：
学科分类号：
摘要：
Fourier continuation (FC) is an approach used to create periodic extensions of non-periodic functions to obtain highly-accurate Fourier expansions. These methods have been used in partial differential equation (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 the stability and the convergence. Here we propose the use of FC in forming a new basis for the DG framework.
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页码：1385 / 1405
页数：20
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