A Conservative and Energy Stable Discontinuous Spectral Element Method for the Shifted Wave Equation in Second Order Form

نویسندگان

چکیده

In this paper, we develop a provably energy stable and conservative discontinuous spectral element method for the shifted wave equation in second order form. The proposed combines advantages central ideas of following very successful numerical techniques: summation-by-parts finite difference method, Galerkin method. We prove stability discrete conservation principle derive error estimates norm (1+1)-dimensions energy-stability results, principle, generalize to multiple dimensions using tensor products quadrilateral hexahedral elements. Numerical experiments, (2+1)-dimensions, verify theoretical results demonstrate optimal convergence $L^2$ errors at subsonic, sonic supersonic regimes.

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ژورنال

عنوان ژورنال: SIAM Journal on Numerical Analysis

سال: 2022

ISSN: ['0036-1429', '1095-7170']

DOI: https://doi.org/10.1137/21m1432922