An ensemble Monte Carlo HDG method for parabolic PDEs with random coefficients

We use Monte Carlo, ensemble and hybrid discontinuous Galerkin method (EMC-HDG) to numerically solve parabolic partial differential equations (PDEs) with random coefficients. The proposed method reduces the computational cost and the storage requirement by solving multiple linear systems with a common coefficient matrix. Error analysis shows the proposed method is first-order accurate in time and optimal L-2 convergence order in physical space. In the end, several numerical experiments are presented to verify the theoretical results.