# Numerical approximation of stochastic evolution equations: Convergence in scale of Hilbert spaces

Bessaih H, Hausenblas E, Randrianasolo TA, Razafimandimby P (2018)
Journal of Computational and Applied Mathematics 343: 250-274.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
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Abstract / Bemerkung
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 $\beta$. }
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Zeitschriftentitel
Journal of Computational and Applied Mathematics
Band
343
Seite(n)
250-274
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Bessaih H, Hausenblas E, Randrianasolo TA, Razafimandimby P. Numerical approximation of stochastic evolution equations: Convergence in scale of Hilbert spaces. Journal of Computational and Applied Mathematics. 2018;343:250-274.
Bessaih, H., Hausenblas, E., Randrianasolo, T. A., & Razafimandimby, P. (2018). Numerical approximation of stochastic evolution equations: Convergence in scale of Hilbert spaces. Journal of Computational and Applied Mathematics, 343, 250-274. doi:10.1016/j.cam.2018.04.067
Bessaih, H., Hausenblas, E., Randrianasolo, T. A., and Razafimandimby, P. (2018). Numerical approximation of stochastic evolution equations: Convergence in scale of Hilbert spaces. Journal of Computational and Applied Mathematics 343, 250-274.
Bessaih, H., et al., 2018. Numerical approximation of stochastic evolution equations: Convergence in scale of Hilbert spaces. Journal of Computational and Applied Mathematics, 343, p 250-274.
H. Bessaih, et al., “Numerical approximation of stochastic evolution equations: Convergence in scale of Hilbert spaces”, Journal of Computational and Applied Mathematics, vol. 343, 2018, pp. 250-274.
Bessaih, H., Hausenblas, E., Randrianasolo, T.A., Razafimandimby, P.: Numerical approximation of stochastic evolution equations: Convergence in scale of Hilbert spaces. Journal of Computational and Applied Mathematics. 343, 250-274 (2018).
Bessaih, Hakima, Hausenblas, Erika, Randrianasolo, Tsiry Avisoa, and Razafimandimby, Paul. “Numerical approximation of stochastic evolution equations: Convergence in scale of Hilbert spaces”. Journal of Computational and Applied Mathematics 343 (2018): 250-274.
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