@article{Yong2025, 
author = {JinJun Yong and Changlun Ye and Xianbing Luo},
title = {A fully discrete HDG ensemble Monte Carlo algorithm for a heat equation under uncertainty},
year = {2025},
journal = {Networks and Heterogeneous Media},
volume = {20},
number = {1},
pages = {65-88},
keywords = {hybridizable discontinuous Galerkin, ensemble approach, Monte Carlo method, diffusion coefficient, Robin boundary coefficient, optimal},
url = {https://www.sciopen.com/article/10.3934/nhm.2025005},
doi = {10.3934/nhm.2025005},
abstract = {This paper has introduced a novel fully discrete hybridizable discontinuous Galerkin (HDG) ensemble Monte Carlo method (FEMC-HDG) tailored for solving the heat equation with random diffusion and Robin coefficients. The FEMC-HDG method solves a single linear system with multiple right-hand side vectors per time step. We established stability analysis and error estimates that are optimal in the spatial and first-order accuracy in time for the        L          ∞        (  0  ,  T  ,      L    2    (  D  )  )-norm error estimate. Numerical experiments were included to confirm the theoretical convergence and showcase the method's efficiency.}
}