海水入浸数值模拟的特征差分方法和最佳阶l^2误差估计

THE CHARACTERISTICSFINITE DIFFERENCE METHODSOF SEA WATER INTRUSION NUMERICAL SIMULATIONAND OPTIMAL ORDER l￣2 ERROR ESTIMATES

滨海含水层中的海水入浸数值模拟和理论分析，是环境科学中十分重要的理论和实际问题，其数学模型是一类三维非线性抛物型偏微分方程组的初、边值问题。一个是关于压力的流动方程，另一个是关于含盐浓度的对流扩散方程．在考虑三维有界区域的一般情况，提出一类特征有限差分格式，利用粗细网块结合，变分形式，先验估计理论和技巧，得到最佳阶ｌ２误差估计结果．

The numerical simulation and theoretical analysis for sea water intrusion incoastal region, it is very important theoretical and practical value for environmental science.The mathematical model can be described by a system of nonlinear partial differelltialequations.One is fluid equation for the pressure, and the other one is advection-dispersionequation in form for the saltwater concentration. For a generic case of three dimensionalbounded region, we put forward a kind of characteristic finite difference schemes and makeuse thick and thin grids to form a complete set,and of calculus of variations, the theory ofprior estimates and techniques.Optimal order estimates in 12 norm are derived for the errorin the approximation solutions.