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.


finite-element methods


semilinear stochastic wave equation

geometric numerical integration

trace formula

additive noise

strong convergence

multiplicative noise

stochastic trigonometric methods


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 1093-1119

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Basic sciences



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