有限元-康托洛维奇杂交法及其应用

Finite Element Kantorovich Combination Method and Its Application

本文将有限元法与康托洛维奇方法进行适当组合,吸收二者的主要优点,提出在单元的位移插值函数中附加康托洛维奇项。康托洛维奇方法是一种半解析法,其在解析方向具有较高的精度,在一定程度上弥补了原有限元方法中插值函数选取的盲目性,能够较好地反映微分方程的固有性质,提高其适应性。在单元的位移插值函数中附加内部无节点的位移项,无需增加新的单元与节点,使用较少的单元即可获得较高的精度。并且,这些附加项满足单元边界条件为零,故其在单元与单元的交界面上是保证协调的。本文通过算例充分说明了此方法的特点和优越性。

Combining finite element method with Kantorovich method and utilizing their advantages, a new method was advanced here. Kantorovich method is a semi-analytical method, it obtained a better accuracy on the analytical direction, which making up the blindness of interpolation function in finite element method and increasing the adaptability of the method. The displacements without inside nodes are added to the displacement insert functions of elements, a better accuracy without more elements was obtained, and it is compatible. Current work showes its superiority by computing illustrations.