Tractability of the Quasi-Monte Carlo quadrature with Halton points for elliptic PDEs with random diffusion

This article is dedicated to the computation of the moments of the solution to stochastic partial differential equations with log-normal distributed diffusion coefficient by the Quasi-Monte Carlo method. Our main result is the polynomial tractability for the Quasi-Monte Carlo method based on the Halton sequence. As a by-product, we obtain also the strong tractability of stochastic partial differential equations with uniformly elliptic diffusion coefficient by the Quasi-Monte Carlo method. Numerical experiments are given to validate the theoretical findings.