论文标题
随机2D Navier-Stokes方程的时空Euler离散化方案
Space-time Euler discretization schemes for the stochastic 2D Navier-Stokes equations
论文作者
论文摘要
我们证明，隐式时间EULER方案以及有限元素空间空间离散化的圆环上的2D Navier-Stokes方程，但要经受$ l^2（ω）$的随机扰动收敛，并描述$ H^1 $ h^1 $ $ h^1 $的初始条件的收敛速率。这完善了先前的结果，该结果仅确定了这些数值近似值的概率。使用随机Navier-Stokes方程的解和局部方案的收敛性的指数力矩估计，我们可以证明该时空近似的强收敛。 $ l^2（ω）$ - 收敛的速度取决于扩散系数和粘度参数。如果是Scott-Vogelius混合元素和加性噪声，则收敛是多项式。
We prove that the implicit time Euler scheme coupled with finite elements space discretization for the 2D Navier-Stokes equations on the torus subject to a random perturbation converges in $L^2(Ω)$, and describe the rate of convergence for an $H^1$-valued initial condition. This refines previous results which only established the convergence in probability of these numerical approximations. Using exponential moment estimates of the solution of the stochastic Navier-Stokes equations and convergence of a localized scheme, we can prove strong convergence of this space-time approximation. The speed of the $L^2(Ω)$-convergence depends on the diffusion coefficient and on the viscosity parameter. In case of Scott-Vogelius mixed elements and for an additive noise, the convergence is polynomial.
