Full Discretization of Semilinear Stochastic Wave Equations Driven by Multiplicative Noise

• 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.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

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

approximation

Publikations- och innehållstyp

ref (ämneskategori)

art (ämneskategori)