Full Discretization of Semilinear Stochastic Wave Equations Driven by Multiplicative Noise
Journal article, 2016
A fully discrete approximation of the semilinear stochastic wave equation driven by multiplicative noise is presented. A standard linear finite element approximation is used in space, and a stochastic trigonometric method is used for the temporal approximation. This explicit time integrator allows for mean-square error bounds independent of the space discretization and thus does not suffer from a step size restriction as in the often used Stormer-Verlet leapfrog 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.
multiplicative noise
semilinear stochastic wave equation
trace formula
partial-differential-equations
finite-element methods
approximation
additive noise
geometric numerical integration
stochastic trigonometric methods
strong convergence
Author
R. Anton
Umea universitet
D. Cohen
Umea universitet
University of Innsbruck
Stig Larsson
University of Gothenburg
Chalmers, Mathematical Sciences, Mathematics
X. Wang
Central South University China
SIAM Journal on Numerical Analysis
0036-1429 (ISSN) 1095-7170 (eISSN)
Vol. 54 2 1093-1119Subject Categories (SSIF 2011)
Mathematics
Roots
Basic sciences
DOI
10.1137/15m101049x