منابع مشابه
Trivariate C Polynomial Macro-Elements
Trivariate C macro-elements defined in terms of polynomials of degree 8r + 1 on tetrahedra are analyzed. For r = 1, 2, these spaces reduce to well-known macro-element spaces used in data fitting and in the finite-element method. We determine the dimension of these spaces, and describe stable local minimal determining sets and nodal minimal determining sets. We also show that the spaces approxim...
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We study Lissajous curves in the 3-cube that generate algebraic cubature formulas on a special family of rank-1 Chebyshev lattices. These formulas are used to construct trivariate hyperinterpolation polynomials via a single 1-d Fast Chebyshev Transform (by the Chebfun package), and to compute discrete extremal sets of Fekete and Leja type for trivariate polynomial interpolation. Applications co...
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We begin with the following question: given a closed disc D ⋐ C and a complex-valued function F ∈ C(D), is the uniform algebra on D generated by z and F equal to C(D) ? When F ∈ C 1 (D), this question is complicated by the presence of points in the surface S := graph D (F) that have complex tangents. Such points are called CR singularities. Let p ∈ S be a CR singularity at which the order of co...
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We begin with the following question: given a closed disc D b C and a complexvalued function F ∈ C(D), is the uniform algebra on D generated by z and F equal to C(D) ? When F ∈ C1(D), this question is complicated by the presence of points in the surface S := graphD(F ) that have complex tangents. Such points are called CR singularities. Let p ∈ S be a CR singularity at which the order of contac...
متن کاملA Cr trivariate macro-element based on the Alfeld split of tetrahedra
We construct trivariate macro-elements of class Cr for any r ≥ 1 over the Alfeld refinement of any tetrahedral partition in R3. In our construction, the degree of polynomials used for these macro-elements is the lowest possible. We also give the dimension formula for the subspace of consisting of these macroelements.
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ژورنال
عنوان ژورنال: Constructive Approximation
سال: 2006
ISSN: 0176-4276,1432-0940
DOI: 10.1007/s00365-006-0631-x