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

Hakima Bessaih and Annie Millet ()
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Hakima Bessaih: Mathematics and Statistics Department, Florida International University, 11200 SW 8th Street, Miami, FL 33199, USA
Annie Millet: Statistique, Analyse et Modélisation Multidisciplinaire, EA 4543, Université Paris 1 Panthéon Sorbonne, Centre Pierre Mendès France, 90 Rue de Tolbiac, CEDEX, 75634 Paris, France

Mathematics, 2022, vol. 10, issue 22, 1-39

Abstract: 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 , 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 ( Ω ) . These results were 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 -norms of the solutions are bounded.

Keywords: Boussinesq model; implicit time Euler schemes; convergence in probability; strong convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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