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

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:343

Article

Bessaih, Hakima¹  Hausenblas, Erika²  Randrianasolo, Tsiry Avisoa³  Razafimandimby, Paul Andre⁴ 

[1] Univ Wyoming, Dept Math, Laramie, WY 82071 USA

[2] Univ Leoben, Lehrstuhl Angew Math, Peter Tunner Str 25-27, A-8700 Leoben, Austria

[3] Bielefeld Univ, Fak Math, Univ Str 25, D-33615 Bielefeld, Germany

[4] Univ Pretoria, Dept Math & Appl Math, Lynwood Rd, ZA-0083 Pretoria, South Africa

关键词: Goy and sabra shell model;    Nonlinear heat equation;    Galerkin approximation;    Fully implicit scheme;    Semi-implicit scheme;    Convergence in probability;   

DOI  :  10.1016/j.cam.2018.04.067

来源: Elsevier

【 摘 要 】

The present paper is devoted to the numerical approximation of an abstract stochastic nonlinear evolution equation in a separable Hilbert space 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 V-beta subset of H with beta is an element of [0, 1/4) and that the explicit rate of convergence of our scheme depends on this parameter beta. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free