An EMC-HDG scheme for the convection-diffusion equation with random diffusivity

In this work, we propose an ensemble Monte Carlo hybridizable discontinuous Galerkin (EMC-HDG) algorithm to simulate the convection-diffusion equation with random diffusion coefficients. The EMC-HDG algorithm reduces the computation cost compared with Monte Carlo HDG (MC-HDG) method. This algorithm is a semi-implicit scheme which shares a common coefficient matrix with multiple right-hand-vectors by introducing an ensemble average of coefficient functions. Moreover, for the numerical approximation, optimal convergence rate O(h(k+ 1)) in space and O(ot) in time are obtained. To confirm our theoretical results, several numerical experiments are also presented.