Projected Multilevel Monte Carlo Method for PDE with random input data

Abstract: The order of convergence of the Monte Carlo method is 1/2 which means that we need quadruple samples to decrease the error in half in the numerical simulation. Multilevel Monte Carlo methods reach the same order of error by spending less computational time than the Monte Carlo method. To reduce the computational complexity further, we introduce a projected multilevel Monte Carlo method. Numerical experiments validate our theoretical results.