Technical Report 2018-012

Eigenvalue Isogeometric Approximations Based on B-splines: Tools and Results

Sven-Erik Ekström and Stefano Serra-Capizzano

July 2018

In such a short note we consider the spectral analysis of large matrices coming from the numerical approximation of the eigenvalue problem
-(a(x)u'(x))'=λ b(x) u(x),     x∈ (0,1),
where u(0) and u(1) are given, by using isogeometric methods based on B-splines. We give precise estimates for the extremal eigenvalues and global distributional results. The techniques involve dyadic decomposition arguments, the GLT analysis, and basic extrapolation methods.

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