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

TL;DR

This paper presents an iterative splitting scheme for 2D stochastic primitive equations with multiplicative noise, demonstrating convergence with a strong speed rate of nearly 1/2, facilitating numerical solutions.

Contribution

It introduces a novel splitting method for stochastic primitive equations and provides convergence analysis with explicit error estimates.

Findings

Convergence rate in probability is nearly 1/2.

Splitting simplifies numerical computation of stochastic primitive equations.

Error estimates support the scheme's effectiveness.

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 $\frac{1}{2}$.