Estimate Analysis of a Fully Discrete Mixed Finite Element Scheme for Stochastic Incompressible Navier-Stokes Equations with Multiplicative Noise
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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 space-time approximation with respect to convergence in probability for the velocity and the pressure are obtained. By using the negative norm technique, the H^1 and L^2 convergence of this scheme for the velocity is derived.
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