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Spline approximations on manifolds. (English) Zbl 1139.65301

A method of construction of the local approximations in the case of functions defined on \(n\)-dimensional \((n\geq 1)\) smooth manifold with boundary is proposed. In particular, spline and finite-element methods on manifold are discussed. Nondegenerate simplicial subdivision of the manifold is introduced and a simple method for evaluations of approach is examined (the evaluations are optimal as to \(N\)-width of corresponding compact set).

MSC:

65D07 Numerical computation using splines
41A15 Spline approximation
65D18 Numerical aspects of computer graphics, image analysis, and computational geometry
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[1] DOI: 10.1137/0726055 · Zbl 0679.41008 · doi:10.1137/0726055
[2] DOI: 10.1090/S0025-5718-1995-1308448-4 · doi:10.1090/S0025-5718-1995-1308448-4
[3] DOI: 10.1007/s003650010034 · Zbl 1004.41005 · doi:10.1007/s003650010034
[4] Strang G., An Analysis of the Finite Element Method (1973) · Zbl 0356.65096
[5] DOI: 10.1007/978-3-0348-5499-3 · doi:10.1007/978-3-0348-5499-3
[6] Ciarlet P., The Finite Element Method for Elliptic Problems (1978) · Zbl 0383.65058
[7] Demjanovich Yu. K., Local Approximation on Manifold and Minimal Splines (1994)
[8] Lions J.-L., Problémes aux Limites non Homogénes et Applications 1 (1968)
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