二维土壤溶质输运方程基于POD方法的降阶CN有限体积元外推算法

A REDUCED-ORDER CN FINITE VOLUME ELEMENT EXTRAPOLATING ALGORITHM BASED ON POD METHOD FOR TWO-DIMENSIONAL SOIL SOLUTE TRANSPORT EQUATIONS

利用Crank-Nicolson(CN)有限体积元方法和特征投影分解方法建立二维土壤溶质输运方程的一种维数很低、精度足够高的降阶CN有限体积元外推算法,并给出这种外推算法的降阶CN有限体积元解的误差估计和算法的实现.最后用数值例子说明数值结果与理论结果相吻合,并阐明这种降阶CN有限体积元外推算法的优越性.

A reduced-order Crank-Nicolson finite volume element （UNFVE） extrapolating algo- rithm with sufficiently high accuracy and fewer dimensions for two-dimensional soil solute transport equations is established by means of the CNFVE method and POD technique. The error estimates of the reduced-order CNFVE solutions and the implementation of the reduced-order CNFVE extrapolating algorithm are provided. Finally, a numerical example is used to illustrate that the results of numerical computation are consistent with theoretical conclusions. Moreover, the advantage of the reduced-order CNFVE extrapolating algorithm is shown.