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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.

MSC:
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)
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