论文标题
分析具有乘法噪声的随机Navier-Stokes方程的完全离散的混合有限元方案
Analysis of fully discrete mixed finite element scheme for Stochastic Navier-Stokes equations with multiplicative noise
论文作者
论文摘要
本文与周期性边界条件有关的随机不可压缩的Navier-Stokes方程在二维中具有乘法噪声。根据乘法噪声的Helmholtz分解，提出了半滴和完全离散的时间步变算法。基于混合有限元方法的收敛速率相对于速度和压力的概率收敛性。此外，通过建立一些稳定性并使用负标准技术，事实证明，$ h^1 $和$ l^2 $规范的部分期望被证明可以最佳收敛。
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 $H^1$ and $L^2$ norms of the velocity error are proved to converge optimally.
