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.
approximation
finite-element methods
partial-differential-equations
semilinear stochastic wave equation
geometric numerical integration
trace formula
additive noise
strong convergence
multiplicative noise
stochastic trigonometric methods
Author
R. Anton
Umeå University
David Cohen
Umeå University
University of Innsbruck
Stig Larsson
Chalmers, Mathematical Sciences, Mathematics
University of Gothenburg
X. Wang
Central South University
SIAM Journal on Numerical Analysis
0036-1429 (ISSN) 1095-7170 (eISSN)
Vol. 54 2 1093-1119Subject Categories
Mathematics
Roots
Basic sciences
DOI
10.1137/15m101049x