An MLMCE-HDG method for the convection diffusion equation with random diffusivity

Abstract

In this paper, a multilevel Monte Carlo ensemble hybridizable discontinuous Galerkin (MLMCE-HDG) method is proposed to solve the convection diffusion equation with random diffusion coefficients. This method combines the MLMC method in probability space, an ensemble approach in time space and the HDG method in physical space. The proposed method possesses a second order accuracy in time space and optimal L 2 convergence rate in physical space. The stability analysis, error estimates and computational cost are provided. Finally, to illustrate the theoretical analyses, several numerical experiments are performed.