Full Discretization of Semilinear Stochastic Wave Equations Driven by Multiplicative Noise
Artikel i vetenskaplig tidskrift, 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

Författare

R. Anton

Umea universitet

D. Cohen

Umea universitet

University of Innsbruck

Stig Larsson

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

X. Wang

Central South University China

SIAM Journal on Numerical Analysis

0036-1429 (ISSN) 1095-7170 (eISSN)

Vol. 54 1093-1119

Ämneskategorier

Matematik

Fundament

Grundläggande vetenskaper

DOI

10.1137/15m101049x