非均匀(Ⅱ)型三角剖分下双周期二次样条空间S21(△mn(2))

Double Periodic Quadratic Spline Space S21(△mn(2)) over the Non-regular Type-2 Triangulation

关键词:  非均匀(Ⅱ)型三角剖分  双周期二次样条空间  维数  基底

Key words:  nonregular type-2 triangulation  double periodic quadratic spline space  dimension  basis

摘要:

设Ω=[0,x_m]⊗[0,y_n」,Ω的熟知的非均匀(Ⅰ)、(Ⅱ)型三角剖分分别记为△_mn⁽ⁱ⁾,i=1,2.△_mn⁽ⁱ⁾上的分片二元k次C¹多项式的全体记为S₂¹(△_mn⁽ⁱ⁾),称为二元k次一阶光滑的样条函数空间.进一步,引入其子空间S₂¹(△_mn⁽ⁱ⁾)={s∈S₂¹(△_mn⁽ⁱ⁾):D^αs(·,0)=D^αs(·,yn),D^αs(0,·)=D^αs(x_m,·),α=0,1}.称为双周期k次样条空间.本文给出了Ω的非均匀(Ⅱ)型三角剖分△_mn⁽²⁾下双周期二次样条空间S₂¹(△_mn⁽²⁾)的维数及一组基底.

Abstract:

Let Ω=[0,x_m] [0, y_n], the well-known nonregular type-2 triangulation of Ω is denoted by △_mn⁽ⁱ⁾,and the space of piecewise C¹ quadratic polynomials is denoted by S₂¹(△_mn⁽ⁱ⁾).Define S₂¹(△_mn⁽ⁱ⁾)={s∈S₂¹(△_mn⁽ⁱ⁾):D^αs(·,0)=D^αs(·,y_n),D^αs(0,·)=D^αs(x_m,·),α=0,1},called double periodic quadratic spline space. In this paper, the dimension and a basis of the space S₂¹(△_mn⁽²⁾) were given.