This paper develops a new 2D/3D stochastic closed-loop geothermal system with a random hydraulic conductivity tensor. We use the finite element method (FEM) and the Monte Carlo method (MCM) to discrete physical and probability spaces, respectively. This FEM-MCM method is effective. The stability for velocity and temperature is rigorously proved. Compared with the deterministic closed-loop geothermal system, a same optimal error estimate for approximate velocity and temperature is obtained. Furthermore, a series of numerical experiments were carried out to show this method has better stability and accuracy results.

翻译：本文建立了一种具有随机水力传导率张量的新型二维/三维随机闭环地热系统。我们分别采用有限元法（FEM）和蒙特卡洛方法（MCM）对物理空间与概率空间进行离散。该FEM-MCM方法具有良好效果。文中严格证明了速度场与温度场的稳定性。与确定性闭环地热系统相比，获得了近似速度场与温度场同等的最优误差估计。此外，通过一系列数值实验验证了该方法具有更优的稳定性与精度结果。