海水入浸问题的数值分析(英文)

Numerical Analyses for Seawater Intrusion Problem

海水入浸问题的数学模型是两个耦合抛物型偏微分方程,其中一个是关于压力的流动方程,另一个是关于浓度的对流扩散方程.压力方程由标准有限元方法逼近,浓度方程则用特征有限元方法逼近.在扩散项系数半正定的情形得到逼近解的次优L2 模误差估计.

Seawater intrusion is modelled as a nonlinear system of coupled two parabolic partial differential euqaitons,of which one is the pressure flow equation and the other one is the concentration equation of convection-dispersion type.The pressure is approximated by a finite element method,and the concentration is approximated by the combination of a Galerkin finite element method and characteristics-finite element method.L2-norm error estimates are derived under the assumption of only positive semi-definite diffusion coefficient.