二维土壤溶质输运方程基于POD方法的降阶CN有限元外推算法

A POD-based Reduced-order CN Finite Element Extrapolating Algorithm for Two-dimensional Soil Solute Transport Equations

首先给出二维土壤溶质输运方程时间二阶精度的Crank-Nicolson(CN)时间半离散化格式和时间二阶精度的全离散化CN有限元格式及其误差分析.然后利用特征投影分解(proper orthogonal decomposition,简记为POD)方法对二维土壤溶质输运方程的经典CN有限元格式做降阶处理,建立一种具有足够高精度、自由度很少的降阶CN有限元外推格式,并给出这种降阶CN有限元解的误差估计和外推算法的实现.最后用数值例子说明数值结果与理论结果是相吻合的.

A Crank-Nicolson(CN) time semi-discrete formulation with second-order time accuracy for two-dimensional soil solute transport equations and a classical fully discrete CN finite element formulation with second-order time accuracy as well as the error estimates of its solutions are provided first.And then,a proper orthogonal decomposition(POD) technique is used to reduce the dimensions of the classical CN finite element formulation for two-dimensional soil solute transport equations,a POD-based reduced-order CN finite element extrapolating formulation with sufficiently high accuracy and fewer degrees of freedom is established,and the error estimates of the reduced-order finite element solutions and the implementation of the extrapolating algorithm are provided.Finally,a numerical example is used to illustrate that the results of numerical computation are consistent with theoretical conclusions.