## A Tree Algorithm for Isotropic Finite Elements on the Sphere

• The Earth's surface is an almost perfect sphere. Deviations from its spherical shape are less than 0,4% of its radius and essentially arise from its rotation. All equipotential surfaces are nearly spherical, too. In consequence, multiscale modelling of geoscientifically relevant data on the sphere involving rotational symmetry of the trial functions used for the approximation plays an important role. In this paper we deal with isotropic kernel functions showing local support and (one-dimensional) polynomial structure (briefly called isotropic finite elements) for reconstructing square--integrable functions on the sphere. Essential tool is the concept of multiresolution analysis by virtue of the spherical up function. The main result is a tree algorithm in terms of (low--order) isotropic finite elements.

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Author: Frank Bauer, Willi Freeden, Michael Schreiner urn:nbn:de:hbz:386-kluedo-12684 Schriften zur Funktionalanalysis und Geomathematik (3) Preprint English 2003 2003 Technische Universität Kaiserslautern 2003/11/10 Locally Supported Radial Basis Functions; Multisresolution Analysis; Spherical; Up Functions Fachbereich Mathematik 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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