Error estimates of finite element methods for nonlinear fractional stochastic differential equations

Abstract

In this paper, we consider the Galerkin finite element approximations of the initial value problem for the nonlinear fractional stochastic partial differential equations with multiplicative noise. We study a spatial semidiscrete scheme with the standard Galerkin finite element method and a fully discrete scheme based on the Goreno–Mainardi–Moretti–Paradisi (GMMP) scheme. We establish strong convergence error estimates for both semidiscrete and fully discrete schemes.