Macro-element Hierarchical Riesz Bases
نویسندگان
چکیده
We show that a nested sequence of C macro-element spline spaces on quasi-uniform triangulations gives rise to hierarchical Riesz bases of Sobolev spaces H(Ω), 1 < s < r+ 3 2 , and H 0(Ω), 1 < s < σ+ 3 2 , s / ∈ Z+ 1 2 , as soon as there is a nested sequence of Lagrange interpolation sets with uniformly local and bounded basis functions, and, in case of H 0(Ω), the nodal interpolation operators associated with the macroelement spaces are boundary conforming of order σ. In addition, we provide a brief review of the existing constructions of C Largange type hierarchical bases.
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