A posteriori analysis of finite element discretizations of stochastic partial differential delay equations

Abstract

In this paper, we study a posteriori error estimates for finite element approximation of stochastic partial differential delay equations containing a noise. We derive an energy norm a posteriori bounds for an Euler time-stepping method combined with a standard Galerkin schemes for the problems. For accessibility, we first address the spatially semidiscrete case and then move to the fully discrete scheme.