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Full Discretization of Semilinear Stochastic Wave Equations Driven by Multiplicative Noise

R. Anton ; D. Cohen ; Stig Larsson (Institutionen för matematiska vetenskaper, matematik) ; X. J. Wang
Siam Journal on Numerical Analysis (0036-1429). Vol. 54 (2016), 2, p. 1093-1119.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: semilinear stochastic wave equation, multiplicative noise, strong convergence, trace formula, stochastic trigonometric methods, geometric numerical integration, partial-differential-equations, finite-element methods, additive noise, approximation



Denna post skapades 2016-05-27. Senast ändrad 2016-07-06.
CPL Pubid: 237018

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Matematik

Chalmers infrastruktur