Communications in Mathematical Sciences

Volume 17 (2019)

Number 2

Splitting up method for 2D stochastic primitive equations with multiplicative noise

Pages: 473 – 505

DOI: https://dx.doi.org/10.4310/CMS.2019.v17.n2.a8

Authors

Xuhui Peng (School of Mathematics and Statistics, Hunan Normal University, Changsha, China)

Rangrang Zhang (School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, China)

Abstract

This paper concerns the convergence of an iterative scheme for 2D stochastic primitive equations on a bounded domain. The stochastic system is split into two equations: a deterministic 2D primitive equations with random initial value and a linear stochastic parabolic equation, which are both simpler for numerical computations. An estimate of approximation error is given, which implies that the strong speed rate of the convergence in probability is almost $\frac{1}{2}$.

Keywords

splitting up method, primitive equations, approximation error, speeding of convergence in probability, stopping time

2010 Mathematics Subject Classification

60H15, 60H30, 76D06, 76M35

Full Text (PDF format)

This work was supported by the National Natural Science Foundation of China (No. 11501195, 11871476, 11801032); the China Postdoctoral Science Foundation funded project (No. 2018M641204); the Key Laboratory of Random Complex Structures and Data Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences (No. 2008DP173182); the Scientific Research Fund of Hunan Provincial Education Department (No. 17C0953); and the Hunan Provincial Natural Science Foundation of China (No. 2019JJ50377).

Received 24 January 2018

Received revised 17 December 2018

Accepted 17 December 2018

Published 8 July 2019