带有齐次边界条件的C^1四次样条空间

C^1 Quartic Spline Spaces with Homogeneous Boundary Conditions

设Q是单连通多边形区域,△为其三角分划。给定整数,次数为d光滑度为r的样条空间(△)定义为 在每一个三角形上其中π_d表示次数为d的多项式空间。本文考虑如下两个子空间当△为可限分划时,给出了这两个子空间的维数及局部支撑基底的构造。

Let Ω be a simply connected polygonal domain and △ denote a triangulation of Ω Given integers 0≤r<d, spline spaces s_d^r(△) of smoothness r and degree d are defined as {s restricted each triangle belongs tO π_d} where π is the spacc of polynomials of total degree d. In thispaper, following subspaees are considered. The dimension and construction of cocaUy supported bases are given when △ is a confinablc triangulation.