非饱和土壤水流问题的CN有限元格式

首先给出二维非饱和土壤水流问题基于Crank-Nicolson(CN)方法的具有时间二阶精度的半离散化格式,然后直接从CN时间半离散化格式出发,建立具有时间二阶精度的全离散化CN有限元格式,并给出误差估计,最后用数值例子说明全离散化CN有限元格式的优越性.这种方法可以绕开关于空间变量的半离散化格式的讨论,提高时间离散的精度,极大地减少时间方向的迭代步,从而减少实际计算中截断误差的积累,提高计算精度和计算效率.

A CN FINITE ELEMENT FORMULATION FOR UNSATURATED SOIL WATER PROBLEM

In this paper, based on Crank-Nicolson (CN) technique, a semi-discrete formulation with respect to time second-order accuracy for two-dimensional unsaturated soil water flow problem is established firstly. And then, a fully discrete CN finite element formulation with time second-order accuracy is directly found from the semi-discrete formulation with respect to time second-order accuracy and the error estimates of its solutions are provided. Finally, a numerical example is presented to show the advantage of fully discrete CN finite element formulation. The approach here avoids the discussion of the semi-discrete formulation with respect to spatial variable and improves time discrete accuracy so that the number of iterative step is greatly lessened and the accumulation of truncation errors in practical calculation is reduced, and the calculation accuracy and computational efficiency are improved.