We study the spectral approximation properties of isogeometric analysis withlocal continuity reduction of the basis. Such continuity reduction results in areduction in the interconnection between the degrees of freedom of the mesh,which allows for large savings in computational requirements during thesolution of the resulting linear system. The continuity reduction results inextra degrees of freedom that modify the approximation properties of themethod. The convergence rate of such refined isogeometric analysis isequivalent to that of the maximum continuity basis. We show how the breaks incontinuity and inhomogeneity of the basis lead to artefacts in the frequencyspectra, such as stopping bands and outliers, and present a unified descriptionof these effects in finite element method, isogeometric analysis, and refinedisogeometric analysis. Accuracy of the refined isogeometric analysisapproximations can be improved by using non-standard quadrature rules. Inparticular, optimal quadrature rules lead to large reductions in the eigenvalueerrors and yield two extra orders of convergence similar to classicalisogeometric analysis.
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