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 is an element of 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 O(p(-3)) and O(p(-2)) times better than that of the pure finite and spectral element schemes respectively.