二维土壤溶质输运问题的CN有限元法

A CN Finite Element Method for Two-dimension Soil Solute Transport Problems

首先给出二维土壤溶质输运问题时间二阶精度的Crank-Nicolson(CN)时间半离散化格式,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CN有限元解的误差分析,最后用数值例子验证全离散化CN有限元格式的优越性.这种方法提高了时间离散的精度,并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.而且方法绕开对空间变量半离散化有限元格式的讨论,使得理论研究更简便.

In this study, a Crank-Nicolson （CN） semi-discrete tormma^lon wlul ~ - order time accuracy for two-dimension soil solute transport problems is established firstly. And then, a fully discrete CN finite element formulation with second-order time accuracy is directly found from a CN semi-discrete formulation with second-order time accuracy and the error estimates of its solutions are provided. Finally, a numerical example is presented to show the advantage of the fully discrete CN finite element formulation. The approach here 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. And it avoids the discussion of the semi- discrete finite element formulation with respect to spatial variable so that its theory analysis is very simple,