An iterative multilevel Monte Carlo finite element method for convection diffusion equation with random coefficients

An iterative multilevel Monte Carlo (IMLMC) finite element method is applied to approximate the solution of a steady convection diffusion equation with random diffusion and convection coefficients. Each of the random coefficients is decomposed into a deterministic term and a small stochastic perturbation. In this way, through a fixed-point iteration, the randomness of the coefficients of the original equation is transferred to the right-hand side. A large number of systems share a common coefficient matrix, which makes it possible to save computational cost. A rigorous convergence analysis and sharp error estimates are provided. Also, to improve the computational efficiency, an antithetic sampling technique is introduced. Some numerical experiments are done to verify the methods. MSC Classification: 35A35 , 35G15 , 65C05 , 65N15 , 74S05