Finite Element Approximations of Stochastic Linear Schr\"{o}dinger equation driven by additive Wiener noise

TL;DR

This paper analyzes finite element methods for approximating solutions to the stochastic linear Schrödinger equation with additive noise, providing error estimates and supporting numerical experiments.

Contribution

It introduces a semi-discrete finite element approach for the stochastic Schrödinger equation and derives new error bounds for the approximation.

Findings

Error estimates for finite element approximation

Numerical experiments confirming theoretical bounds

Effective spatial discretization for stochastic PDEs

Abstract

In this article, we have analyzed semi-discrete finite element approximations of the Stochastic linear Schr\"{o}dinger 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.