Speed of Convergence of Time Euler Schemes for a Stochastic 2D Boussinesq Model
Speed of Convergence of Time Euler Schemes for a Stochastic 2D Boussinesq Model
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DOI：
10.3390/math10224246
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发表时间：
2022-10
期刊：
影响因子：
2.4
通讯作者：
H. Bessaih;A. Millet
中科院分区：
文献类型：
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作者：
H. Bessaih;A. Millet
我们证明了二维Boussinesq模型在环面D上的隐式时间Euler格式的收敛性。计算了速度和温度的W1，2-范数的各种矩及其离散化。我们得到了最优的概率收敛速度和对数L2（Ω）收敛速度。这些结果是由解在L2（D）和W1，2（D）中的时间正则性以及解的W1，2-范数有界的子集的L2（Ω）收敛性导出的.
We prove that an implicit time Euler scheme for the 2D Boussinesq model on the torus D converges. The various moments of the W1,2-norms of the velocity and temperature, as well as their discretizations, were computed. We obtained the optimal speed of convergence in probability, and a logarithmic speed of convergence in L2(Ω). These results were deduced from a time regularity of the solution both in L2(D) and W1,2(D), and from an L2(Ω) convergence restricted to a subset where the W1,2-norms of the solutions are bounded.