Fourier continuation discontinuous Galerkin methods for linear hyperbolic problems
Published in Communications on Applied Mathematics and Computation, 2022
Recommended citation: van der Sande, K. and Appelo, D. and Albin, N. (2022). “Fourier continuation discontinuous Galerkin methods for linear hyperbolic problems”. Accepted 2022. https://arxiv.org/pdf/2105.00123.pdf
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.
Recommended citation: van der Sande, K. and Appelo, D. and Albin, N. (2022). “Fourier continuation discontinuous Galerkin methods for linear hyperbolic problems”. Accepted 2022.