函数类W^1_p(Ω)到Lagrange型有限元空间插值算子

Interpolation from function space W^1_p(Ω) to Lagrange finite element space

文章给出一种新的方法构造出W1p(Ω)到Lagrange型有限元空间Vh的插值算子,与已有的一般理论相比,该方法有插值算子是完全显式的;插值系数与Vh的基函数无关、插值系数是逐单元进行而非逐点进行且同时算子具有最优逼近阶性质等优点。

<Abstrcat>In this paper a new method is given to construct the interpolation operator from W~~1__p(Ω) to the Lagrange finite element space. In comparison with the known general theories, the presented method has the following advantages:(1) the interpolation operator is completely explicit;(2) the interpolation nodal values are not related to the basis of V_h; and (3) the interpolation nodal values are computed element by element instead of point by point. And the interpolation operator has approximation properties of optimal order. Therefore the interpolation operator given in this paper is easy to construct and convenient to use.