论文标题
随机2D BousSinesQ模型的时间收敛速度
Speed of convergence of time Euler schemes for a stochastic 2D Boussinesq model
论文作者
论文摘要
我们证明，托鲁斯$ d $收敛的2D-Boussinesq模型的隐式时间Euler方案。计算$ W^{1,2} $的各种力矩 - 速度和温度的规范及其离散量。我们获得了概率收敛的最佳速度，以及$ l^2（ω）$的收敛速度。这些结果都是从$ l^2（d）$和$ w^{1,2}（d）$中的解决方案的时间规律性中推导的，以及从$ w^{1,2} $的子集的$ l^2（ω）$收敛限制为solutions的$ w^{1,2} $。
We prove that an implicit time Euler scheme for the 2D-Boussinesq model on the torus $D$ converges. Various moment of the $W^{1,2}$-norms of the velocity and temperature, as well as their discretizations, are computed. We obtain the optimal speed of convergence in probability, and a logarithmic speed of convergence in $L^2(Ω)$. These results are deduced from a time regularity of the solution both in $L^2(D)$ and $W^{1,2}(D)$, and from an $L^2(Ω)$ convergence restricted to a subset where the $W^{1,2}$-noms of the solutions are bounded.
