Fourier Continuation Discontinuous Galerkin Methods for Linear Hyperbolic Problems
Kiera van der Sande, Daniel Appelö, Nathan Albin
Communications on Applied Mathematics and Computation ›› 2022, Vol. 5 ›› Issue (4) : 1385-1405.
Fourier Continuation Discontinuous Galerkin Methods for Linear Hyperbolic Problems
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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