Numerical approximation of stochastic evolution equations: Convergence in scale of Hilbert spaces
Bessaih, Hakima
Bessaih
Hakima
Hausenblas, Erika
Hausenblas
Erika
Randrianasolo, Tsiry Avisoa
Randrianasolo
Tsiry Avisoa
Razafimandimby, Paul
Razafimandimby
Paul
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 $\beta$. }
343
250-274
250-274
Elsevier
2018