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01.06.2015

Cubature rules for harmonic functions based on Radon projections

verfasst von: Irina Georgieva, Clemens Hofreither

Erschienen in: Calcolo | Ausgabe 2/2015

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Abstract

We construct a class of cubature formulae for harmonic functions on the unit disk based on line integrals over \(2n+1\) distinct chords. These chords are assumed to have constant distance \(t\) to the center of the disk, and their angles to be equispaced over the interval \([0,2\pi ]\). If \(t\) is chosen properly, these formulae integrate exactly all harmonic polynomials of degree up to \(4n+1\), which is the highest achievable degree of precision for this class of cubature formulae. For more generally distributed chords, we introduce a class of interpolatory cubature formulae which we show to coincide with the previous formulae for the equispaced case. We give an error estimate for a particular cubature rule from this class and provide numerical examples.

Vorheriger Artikel Stabilized extended finite elements for the approximation of saddle point problems with unfitted interfaces

Nächster Artikel A solution procedure for constrained eigenvalue problems and its application within the structural finite-element code NOSA-ITACA

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Titel: Cubature rules for harmonic functions based on Radon projections
verfasst von: Irina Georgieva
Clemens Hofreither
Publikationsdatum: 01.06.2015
Verlag: Springer Milan
Erschienen in: Calcolo / Ausgabe 2/2015
Print ISSN: 0008-0624
Elektronische ISSN: 1126-5434
DOI: https://doi.org/10.1007/s10092-014-0111-2

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