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.

semilinear stochastic wave equation

geometric numerical integration

trace formula

stochastic trigonometric methods

additive noise

finite-element methods

strong convergence

approximation

partial-differential-equations

multiplicative noise

Författare

R. Anton

Umeå universitet

D. Cohen

University of Innsbruck

Umeå universitet

Stig Larsson

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

X. Wang

Central South University

SIAM Journal on Numerical Analysis

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

Vol. 54 2 1093-1119

Ämneskategorier

Matematik

Fundament

Grundläggande vetenskaper

DOI

10.1137/15m101049x

Mer information

Senast uppdaterat

2018-02-27