Stochastic exponential integrator for finite element spatial discretization of stochastic elastic equation

We investigate the strong convergence of a full discretization for the stochastic elastic equation driven by multiplicative noise. Finite element method is used for the spatial approximation and an exponential integrator scheme is proposed for the temporal discretization. We show that the fully discrete scheme strongly converges to the mild solution of the continuous problem, with precise convergence rates given. As shown in our result, the exponential integrator scheme achieves a higher strong convergence rate than the backward Euler method does in the literature.