Analysis of fully discrete mixed finite element scheme for Stochastic Navier-Stokes equations with multiplicative noise

2022/03/16 by Qiu, Hailong · 1 citation
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2203.08451

Abstract

This paper is concerned with stochastic incompressible Navier-Stokes equations with multiplicative noise in two dimensions with respect to periodic boundary conditions. Based on the Helmholtz decomposition of the multiplicative noise, semi-discrete and fully discrete time-stepping algorithms are proposed. The convergence rates for mixed finite element methods based time-space approximation with respect to convergence in probability for the velocity and the pressure are obtained. Furthermore, with establishing some stability and using the negative norm technique, the partial expectations of the H¹ and L² norms of the velocity error are proved to converge optimally.

Cited by

• Full moment error estimates in strong norms for numerical approximations of stochastic Navier-Stokes equations with multiplicative noise, Part I: time discretization

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