Analysis of Fully Discrete Mixed Finite Element Methods for Time-dependent Stochastic Stokes Equations with Multiplicative Noise

This paper is concerned with fully discrete mixed finite element approximations of the time-dependent stochastic Stokes equations multiplicative noise. A prototypical method, which comprises Euler–Maruyama scheme for time discretization and Taylor-Hood spatial studied in detail. Strong convergence rates established not only velocity approximation but also pressure (in a time-averaged fashion). inf-sup condition used nonstandard way to obtain error estimate fashion. Numerical results are provided validate theoretical gauge performance proposed methods.