We considered an hybridizable discontinuous Galerkin (HDG) method for discrete elliptic PDEs with random coefficients. By an approach of projection, we obtained the error analysis under the assumption that $a(\omega ,x)$ is uniformly bounded. Together with the HDG method, we applied a multilevel Monte Carlo (MLMC) method (MLMC-HDG method) to simulate the random elliptic PDEs. We derived the overall convergence rate and total computation cost estimate. Finally, some numerical experiments are presented to confirm the theoretical results.

中文翻译：

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具有随机系数的椭圆型偏微分方程的MLMC-HDG方法的收敛性分析和成本估计

我们考虑了具有随机系数的离散椭圆PDE的可杂交不连续Galerkin（HDG）方法。通过一种投影的方法，我们在以下假设下获得了误差分析：$\mathrm{一种}（\omega ，X）$是一致有界的。与HDG方法一起，我们应用了多级蒙特卡洛（MLMC）方法（MLMC-HDG方法）来模拟随机椭圆PDE。我们得出了总体收敛速度和总计算成本估算值。最后，通过一些数值实验验证了理论结果。