Convergence Analysis and Cost Estimate of an MLMC-HDG Method for Elliptic PDEs with Random Coefficients
Convergence Analysis and Cost Estimate of an MLMC-HDG Method for Elliptic PDEs with Random Coefficients
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DOI：
10.3390/math9091072
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发表时间：
2021-05
影响因子：
5
通讯作者：
Meng Li;Xianbing Luo
中科院分区：
文献类型：
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作者：
Meng Li;Xianbing Luo
考虑了一类离散椭圆型随机偏微分方程的可杂交间断Galerkin（HDG）方法.在a（ω，x）一致有界的假设下，利用投影方法得到了误差分析.结合HDG方法，我们应用多层蒙特卡罗（MLMC）方法（MLMC-HDG方法）模拟随机椭圆偏微分方程。我们推导出了总的收敛速度和总的计算成本估计。最后，给出了一些数值实验来验证理论结果。
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(ω,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.