Finite Element and Discontinuous Galerkin Method for Stochastic Helmholtz Equation in Two- and Three-Dimensions

Abstract

In this paper, we consider the finite element method and discontinuous Galerkin method for the stochastic Helmholtz equation in $\mathbb{R}^d$ ($d$=2,3). Convergence analysis and error estimates are presented for the numerical solutions. The effects of the noises on the accuracy of the approximations are illustrated. Numerical experiments are carried out to verify our theoretical results.