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

作　　者：袁益让[1] 梁栋[1] 芮洪兴[1] 王高洪 

机构地区：[1]山东大学数学研究所

出　　处：《应用数学学报》1996年第3期395-404,共10页Acta Mathematicae Applicatae Sinica

基　　金：国家攀登计划项目;国家"八五"攻关项目;国家教委博士点基金

摘　　要：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.

关 键 词：海水入浸 误差估计 数值模拟 特征差分法 

分 类 号：P731.27[天文地球—海洋科学]