Reduced basis method for the adapted mesh and Monte Carlo methods applied to an elliptic stochastic problem

Abstract

In this paper, we consider a stochastic elliptic partial differential system and we aim to approximate the solution using the Monte Carlo method based on the finite elements method. To speed up the resolution and reduce the CPU time of computation, we propose to couple the reduced basis method with the adapted mesh method based on an a posteriori error estimate. Balancing the discretization and the Monte Carlo errors is very important to avoid performing an excessive number of iterations. Numerical experiments show and confirm the efficiency of our proposed algorithm.