In this paper, the coupled advection-dominated diffusion-reaction equations which arise in the prevention of groundwater contamination problem are approximated by usual finite element method (FEM). It is clear that by increasing the number of elements to improve computational accuracy, we have to incur a lot of costs. The main presented idea is to reduce the used CPU time for employing the finite-element method by combining that with a technique which reduces the dimension of the problem. To this end, we apply the proper orthogonal decomposition (POD) technique to the usual FEM for the prevention of groundwater contamination problem to reduce CPU time with acceptable accuracy. Numerical examples are provided to illustrate efficiency and validity of the proposed method.

在本文中，在预防地下水污染问题中出现的耦合对流主导的扩散反应方程通过通常的有限元方法（FEM）来近似。很明显，通过增加元素数量来提高计算精度，我们必须承担大量成本。主要提出的想法是通过将有限元方法与降低问题维数的技术相结合来减少使用有限元方法的 CPU 时间。为此，我们将适当的正交分解 (POD) 技术应用于通常的 FEM 以防止地下水污染问题，以在可接受的精度下减少 CPU 时间。提供了数值例子来说明所提出方法的效率和有效性。