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

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