Full Discretization of Semilinear Stochastic Wave Equations Driven by Multiplicative Noise

A fully discrete approximation of the semi-linear stochastic wave equation driven by multiplicative noise is presented. A standard linear finite element approximation is used in space and a stochastic trigonometric method for the temporal approximation. This explicit time integrator allows for mean-square error bounds independent of the space discretisation and thus do not suffer from a step size restriction as in the often used Störmer-Verletleap-frog scheme. Furthermore, it satisfies an almost trace formula (i. e., a linear drift of the expected value of the energy of the problem). Numerical experiments are presented and confirm the theoretical results.