Finite Element Approximations of Stochastic Linear Schrödinger equation driven by additive Wiener noise

In this article, we have analyzed semi-discrete finite element approximations of the Stochastic linear Schrödinger equation in a bounded convex polygonal domain driven by additive Wiener noise. We use the finite element method for spatial discretization and derive an error estimate with respect to the discretization parameter of the finite element approximation. Numerical experiments have also been performed to support theoretical bounds.