A Serendipity Family of Locally Supported Splines in S 28 ( 4 )
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چکیده
For a given triangulation 4 of a region R of interest, let S 2 8 (4) := fs 2 C 2 (R) : sj t 2 IP 8 ; 8t 2 4g be the space of all splines of degree 8 and smoothness 2, where t denotes any triangle of 4 and IP 8 the space of polynomials of total degree 8. Furthermore, let b S 2 8 (4) := fs 2 S 2 8 (4) : s 2 C 3 at v;8v 2 4g be a super spline subspace of S 2 8 (4). We construct a collection of locally supported splines in S 2 8 (4) which can be used to achieve the full approximation order of S 2 8 (4) and its cardinality is less than the dimension of super spline space b S 2 8 (4).
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تاریخ انتشار 2007