Speed of Convergence of Time Euler Schemes for a Stochastic 2D Boussinesq Model

被引：1
|
作者：
Bessaih, Hakima [1 ]
Millet, Annie [2 ,3 ]
机构：
[1] Florida Int Univ, Math & Stat Dept, 11200 SW 8th St, Miami, FL 33199 USA
[2] Univ Paris 1 Pantheon Sorbonne, Ctr Pierre Mendes France, EA 4543, Stat Anal & Modelisat Multidisciplinaire, 90 Rue Tolbiac, F-75634 Paris, France
[3] Univ Paris 6 Paris 7, Lab Probabilites Stat & Modelisat, UMR 8001, Pl Aurelie Nemours, F-75013 Paris, France
来源：
MATHEMATICS | 2022年 / 10卷 / 22期
关键词：
Boussinesq model; implicit time Euler schemes; convergence in probability; strong convergence;
D O I：
10.3390/math10224246
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove that an implicit time Euler scheme for the 2D Boussinesq model on the torus D converges. The various moments of the W-1,W-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 L-2 (Omega). These results were deduced from a time regularity of the solution both in L-2 (D) and W-1,W-2 (D), and from an L-2 (Omega) convergence restricted to a subset where the W-1,W-2 -norms of the solutions are bounded.
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页数：39
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