单纯形上的受限制插值及在有限元中的应用

Interpolations on a Simplex with Constrains and its Applications to Finite Element

形函数空间的选取是单元构造的重要环节 ,有限单元 K上形函数空间 PK 一般是 K上某个 m次多项式空间 Pm(K)的子空间 ,同时要求 PK包含完整的低次多项式空间 Pm -1 (K) ,这成为一个受限制插值问题 .考虑单纯形单元 ,多项式空间采用面积坐标的齐次基函数 ,本文研究了这类受限制插值问题 ,给出 Pm -1 (K) PK Pm(K)的约束条件是充分必要的 ,提出构造 9参三角形板元的新途径 .

In this paper interpolations on a simplex with constrains are studied. The conditions satisfying P m-1 (K)P KP m(K) (K is the element, P k is the shape function space and P m(K) is the polynomial space of degree ≤m) are derived and a new method to construct shape function spaces is presented.