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• W3178702969 abstract "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 method combines the advantages and central ideas of the following very successful numerical techniques: the summation-by-parts finite difference method, the spectral method, and the discontinuous Galerkin method. We prove energy stability and the discrete conservation principle and derive error estimates in the energy norm for the (1+1)-dimensions shifted wave equation in second order form. The energy-stability results, discrete conservation principle, and the error estimates generalize to multiple dimensions using tensor products of quadrilateral and hexahedral elements. Numerical experiments, in (1+1)-dimensions and (2+1)-dimensions, verify the theoretical results and demonstrate optimal convergence of $L^2$ numerical errors at subsonic, sonic and supersonic regimes." @default.
• W3178702969 created "2021-07-19" @default.
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• W3178702969 date "2022-07-05" @default.
• W3178702969 modified "2023-09-25" @default.
• W3178702969 title "A Conservative and Energy Stable Discontinuous Spectral Element Method for the Shifted Wave Equation in Second Order Form" @default.
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• W3178702969 doi "https://doi.org/10.1137/21m1432922" @default.
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