两个带变时间步的两重网格算法的稳定性分析

摘要

This paper represents two types of fully discrete finite element algorithms and two-grid algorithms with variable time steps for numerically solving nonlinear evolution equations in which spatial discretization is made by finite element algorithm, time discretization is done by the Euler explicit different scheme with the first order accuracy and two-step semi-implicit different scheme with the second order accuracy. According to the stability analysis, we find that for the Euler difference scheme and two-step difference scheme on time discretization, the stability of the fully discretization two-grid algorithms is superior to ones of the fully discretization finite element algorithms.%对用于求解非线性发展方程的两个带变时间步的两重网格算法,对空间变量用有限元离散,对时间变量分别用一阶精度Euler显式和二阶精度半隐式差分格式离散,然后构造两重网格算法.通过深入的稳定性分析,得出本文的算法优于标准全离散有限元算法.