Duality and unified analysis of discrete approximations in structural dynamics and wave propagation: comparison of p-method finite elements with k-method NURBS. (English summary) Comput. Methods Appl. Mech. Engrg. 197 (2008), no. 49-50, 4104–4124. The discretization behavior of classical finite element and non-uniform rational B-splines (NURBS) approximations on problems of structural vibration and wave propagation is studied in this paper. Smooth basis functions generated by isogeometric analysis are investigated and compared with standard finite elements. The problems used for comparison emanate from structural dynamics and wave propagation, in particular the eigenvalue problem of free vibration and the Helmholtz equation of time harmonic wave propagation. The basis of comparison is the number of degrees-of-freedom in the discrete model, which turns out to be equivalent to the bandwidth of the corresponding matrix problem. A duality principle is used to map results of spectral analysis to dispersion analysis, and vice versa (though subtle differences between spectrum and dispersion analysis are noted). It is found that NURBS have superior approximation properties. It is observed that the high mode behavior of classical finite elements is divergent with the order of approximation
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