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有限差分法和有限单元(指线性单元,以下同)法是目前解地下水运动偏微分方程最常用的两种数值方法。这两种方法对渗流问题来说究竟那一种更好一些,一直没有定论。由于有限单元法是一种比较新的方法,它从一开始就采用了比较灵活的三角形单元,所以给人们一种印象:似乎有限单元法比有限差分法好。然而许多人的实践表明:前者的精度并不比后者高。加上有限单元法的数学概念比较抽象,运算比较
The finite difference method and the finite element (referring to the linear element, the same below) method are the two most commonly used numerical methods for solving partial differential equations of groundwater movement. These two methods are the better ones for the seepage problem. There has been no conclusion. Since the finite element method is a relatively new method, it uses relatively flexible triangular elements from the beginning, so it gives people an impression that it seems that the finite element method is better than the finite difference method. However, many people’s practice shows that the accuracy of the former is not higher than that of the latter. The mathematical concept of the finite element method is more abstract and computational.