A fully discrete HDG ensemble Monte Carlo algorithm for a heat equation under uncertainty

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 $L^{\mathrm{\infty }}(0,T,L^2(D))$-norm error estimate. Numerical experiments were included to confirm the theoretical convergence and showcase the method's efficiency.