A trigonometric method for the linear stochastic wave equation
Numerical Analysis
2013-03-05 v2
Abstract
A fully discrete approximation of the linear stochastic wave equation driven by additive noise is presented. A standard finite element method is used for the spatial discretisation and a stochastic trigonometric scheme for the temporal approximation. This explicit time integrator allows for error bounds independent of the space discretisation and thus do not have a step size restriction as in the often used St\"ormer-Verlet-leap-frog scheme. Moreover it enjoys a trace formula as does the exact solution of our problem. These favourable properties are demonstrated with numerical experiments.
Cite
@article{arxiv.1203.3668,
title = {A trigonometric method for the linear stochastic wave equation},
author = {D. Cohen and S. Larsson and M. Sigg},
journal= {arXiv preprint arXiv:1203.3668},
year = {2013}
}
Comments
Minor revisions of the previous version (typos, add of references, revised version of the proof of Theorem 4.2)