@inbook{5807b04839c747b38bae8a44da7bb097,

title = "Explicit discrete dispersion relations for the acoustic wave equation in d-dimensions using finite element, spectral element and optimally blended schemes",

abstract = "We study the dispersive properties of the acoustic wave equation for finite element, spectral element and optimally blended schemes using tensor product elements defined on rectangular grid in d-dimensions. We prove and give analytical expressions for the discrete dispersion relations for the above mentioned schemes. We find that for a rectangular grid (a) the analytical expressions for the discrete dispersion error in higher dimensions can be obtained using one dimensional discrete dispersion error expressions; (b) the optimum value of the blending parameter is p/(p + 1) for all p ∈ ℕ and for any number of spatial dimensions; (c) the optimal scheme guarantees two additional orders of accuracy compared with both finite and spectral element schemes; and (d) the absolute accuracy of the optimally blended scheme is and times better than that of the pure finite and spectral element schemes respectively.",

keywords = "acoustic wave equation , finite element analysis , spectral elements",

author = "Mark Ainsworth and Wajid, {Hafiz Abdul} and {Support of MA by the Engineering and Physical Sciences Research Council under grant (Funder)}",

year = "2010",

doi = "10.1007/978-3-642-05241-5_1",

language = "English",

volume = "1",

series = "Computer Methods in Mathematics: Advanced Structured Materials",

publisher = "Springer",

pages = "3--17",

booktitle = "Computer Methods in Mathematics",

edition = "1",

}