Differential Quadrature Hierarchical Finite Element Method, A by Bo Liu;Cuiyun Liu;Yang Wu;Yufeng Xing;

Author:Bo Liu;Cuiyun Liu;Yang Wu;Yufeng Xing;
Language: eng
Format: epub
ISBN: 9789811236778
Publisher: World Scientific Publishing Company
Published: 2021-06-15T00:00:00+00:00

6.1.1Blending function interpolation on a unit square domain

As shown in Fig. 6.2(a), consider a smooth function F(ξ, η) that is defined on a unit square domain with the following boundary functions of values and derivatives:

Fig. 6.2. Blending function interpolation on a unit square domain: (a) boundary functions of values and derivatives; (b) interpolation along the ξ-direction; (c) interpolation along the η-direction.

where Fξ and Fη denote the first-order partial derivatives with respect to ξ and η. The Hermite blending function interpolation can be used to find an approximation function, denoted as F(ξ, η), that has the same boundary functions of values and derivatives as F(ξ, η). To this end, the following third-order Hermite interpolation bases are often used:

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