Stability analysis of high order methods for the wave equation
Weber, Ivy 1Kreiss, Gunilla 1Nazarov, Murtazo1
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作者信息
1. Uppsala Univ
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Abstract
In this paper, we investigate the stability of a numerical method for solving the wave equation. The method uses explicit leap-frog in time and high order continuous and discontinuous (DG) finite elements using the standard Lagrange and Hermite basis functions in space. Matrix eigenvalue analysis is used to calculate time-step restrictions. We show that the time-step restriction for continuous Lagrange elements is independent of the nodal distribution, such as equidistributed Lagrange nodes and Gauss-Lobatto nodes. We show that the time-step restriction for the symmetric interior penalty DG schemes with the usual penalty terms is tighter than for continuous Lagrange finite elements. Finally, we conclude that the best time-step restriction is obtained for continuous Hermite finite elements up to polynomial degrees p = 13. (C) 2021 The Author(s). Published by Elsevier B.V.
NSTL
Elsevier