Fourier Continuation Discontinuous Galerkin Methods for Linear Hyperbolic Problems  

作　　者：Kiera van der Sande Daniel Appelö Nathan Albin 

机构地区：[1]Department of Applied Mathematics,University of Colorado Boulder,Boulder,CO,USA [2]Department of Computational Mathematics,Science&Engineering,Michigan State University,East Lansing,USA [3]Department of Mathematics,Michigan State University,East Lansing,USA [4]Department of Mathematics,Kansas State University,Manhattan,KS,USA

出　　处：《Communications on Applied Mathematics and Computation》2023年第4期1385-1405,共21页应用数学与计算数学学报（英文）

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.

关 键 词：Discontinuous Galerkin Fourier continuation(FC) High order method 

分 类 号：O17[理学—数学]