Fourier Analyses of High-Order Continuous and Discontinuous Galerkin Methods
- Univ. of Lyon (France)
- Univ. of Grenoble (France)
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
In this paper, we present a Fourier analysis of wave propagation problems subject to a class of continuous and discontinuous discretizations using high-degree Lagrange polynomials. This allows us to obtain explicit analytical formulas for the dispersion relation and group velocity and, for the first time to our knowledge, characterize analytically the emergence of gaps in the dispersion relation at specific wavenumbers, when they exist, and compute their specific locations. Wave packets with energy at these wavenumbers will fail to propagate correctly, leading to significant numerical dispersion. We also show that the Fourier analysis generates mathematical artifacts, and we explain how to remove them through a branch selection procedure conducted by analysis of eigenvectors and associated reconstructed solutions. The higher frequency eigenmodes, named erratic in this study, are also investigated analytically and numerically.
- Research Organization:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA); French National Research Agency
- Grant/Contract Number:
- AC04-94AL85000; NA0003525; ANR-14-CE23-0010
- OSTI ID:
- 1725844
- Report Number(s):
- SAND-2020-11694J; 692226
- Journal Information:
- SIAM Journal on Numerical Analysis, Vol. 58, Issue 3; ISSN 0036-1429
- Publisher:
- Society for Industrial and Applied MathematicsCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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