Numerical approximation of stochastic evolution equations: Convergence in scale of Hilbert spaces
Bessaih, Hakima
Hausenblas, Erika
Randrianasolo, Tsiry Avisoa ; https://orcid.org/0000-0002-9413-5189
Razafimandimby, Paul
Goy and Sabra shell model
nonlinear heat equation
Galerkin approximation
time discretization
fully implicit scheme
semi-implicit scheme
convergence in probability
ddc:510
The present paper is devoted to the numerical approximation of an abstract stochastic nonlinear evolution equation in a separable Hilbert space {$\mathrm{H}$}. Examples of equations which fall into our framework include the GOY and Sabra shell models and { a class of nonlinear heat equations.} The space-time numerical scheme is defined in terms of a Galerkin approximation in space and a { semi-implicit Euler--Maruyama scheme in time}. {We prove the convergence in probability of our scheme by means of an estimate of the error on a localized set of arbitrary large probability.} Our error estimate is shown to hold in a more regular space $\mathrm{V}_{\beta}\subset \mathrm{H}$ with $\beta \in [0,\frac14)$ and { that the explicit rate of convergence of our scheme depends on this parameter $\beta$. }
Elsevier
2018
info:eu-repo/semantics/article
doc-type:article
text
https://pub.uni-bielefeld.de/record/2919151
Bessaih H, Hausenblas E, Randrianasolo TA, Razafimandimby P. Numerical approximation of stochastic evolution equations: Convergence in scale of Hilbert spaces. <em>Journal of Computational and Applied Mathematics</em>. 2018;343:250-274.
eng
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.cam.2018.04.067
info:eu-repo/semantics/altIdentifier/issn/1879-1778
info:eu-repo/semantics/altIdentifier/wos/000437820000019
info:eu-repo/semantics/altIdentifier/arxiv/1610.04384
https://creativecommons.org/licenses/by/3.0/