  We study the spectral approximation properties of isogeometric analysis with
local continuity reduction of the basis. Such continuity reduction results in a
reduction in the interconnection between the degrees of freedom of the mesh,
which allows for large savings in computational requirements during the
solution of the resulting linear system. The continuity reduction results in
extra degrees of freedom that modify the approximation properties of the
method. The convergence rate of such refined isogeometric analysis is
equivalent to that of the maximum continuity basis. We show how the breaks in
continuity and inhomogeneity of the basis lead to artefacts in the frequency
spectra, such as stopping bands and outliers, and present a unified description
of these effects in finite element method, isogeometric analysis, and refined
isogeometric analysis. Accuracy of the refined isogeometric analysis
approximations can be improved by using non-standard quadrature rules. In
particular, optimal quadrature rules lead to large reductions in the eigenvalue
errors and yield two extra orders of convergence similar to classical
isogeometric analysis.
