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Duality and unified analysis of discrete approximations in structural dynamics and wave propagation: comparison of p-method finite elements with \(k\)-method NURBS. (English) Zbl 1194.74114
Summary: We study the discretization behavior of classical finite element and NURBS approximations on problems of structural vibrations and wave propagation. We find that, on the basis of equal numbers of degrees-of-freedom and bandwidth, NURBS have superior approximation properties. In fact, we observe that the high mode behavior of classical finite elements is divergent with the order of approximation, a surprisingly negative result. On the other hand, NURBS offer almost spectral approximation properties, and all modes converge with increasing order of approximation.

74H15 Numerical approximation of solutions of dynamical problems in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
Full Text: DOI
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