水污染问题特征有限差分方法的数值计算及理论分析

Numerical analysis of characteristic finite element difference method for water contamination problem

研究水污染二维对流占优数学模型特征有限差分方法的计算问题 ,导出的计算格式对时间变量用特征线修正方法离散 ,对空间变量用带权二阶中心差分方法离散 .对Neumann型边界条件的离散 ,在线性特征差分格式中用一阶偏心差商离散 ,在二次特征差分格式中用一阶中心差商离散 ,在收敛性分析中用离散Green公式处理Neumann型边界条件的影响 ,最后分别得到线性特征差分格式和二次特征差分格式的离散l2

Characteristic finite difference method solving two-dimentional convection-dominated water contamination problem is considered. The schemes combine the centered weighted second order difference discretization in the space variables with the characteristic discretization in the time variables. The first order forward and backward differences are used to treat with the Neumann boundary condition in the characteristic finite difference scheme based on linear interpolation and the first order centered differences are used in the characteristic finite difference scheme based on quadratic interpolation. Also, the discrete Green formula is used to treat the effect of the Neumann boundary condition. The discrete l 2-norm error estimates, which are both optimal order results, are derived for the mentioned two schemes respectively.