Full discretization of semilinear stochastic wave equations driven by multiplicative noise
2016 (English)In: SIAM Journal on Numerical Analysis, ISSN 0036-1429, E-ISSN 1095-7170, Vol. 54, no 2, 1093-1119 p.Article in journal (Refereed) PublishedText
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.
Place, publisher, year, edition, pages
2016. Vol. 54, no 2, 1093-1119 p.
semilinear stochastic wave equation, multiplicative noise, strong convergence, trace formula, stochastic trigonometric methods, geometric numerical integration
Probability Theory and Statistics
IdentifiersURN: urn:nbn:se:umu:diva-121620DOI: 10.1137/15M101049XISI: 000375488100024OAI: oai:DiVA.org:umu-121620DiVA: diva2:940138