Monday, July 10, 2023 - 14:30 in ZiF
Rate of convergence to time Euler scheme for a 2D Boussinesq model
A talk in the SPDEs, optimal control and mean field games series by
| Abstract: |
We prove that an implicit time Euler scheme for the 2D-Boussinesq model on the
torus D converges. Various moments of the $W^{1,2}(D)$-norms of the velocity and
temperature, as well as their discretizations, are computed. We obtain the optimal
rate of convergence in probability, and a logarithmic one for the convergence
in $L^2(\Omega)$. These results are deduced from a time regularity of the solution both
in $L^2(D)$ and $W^{1,2}(D)$, and from an $L^2(\Omega)$ convergence restricted to a subset where
the $W^{1,2}(D)$-noms of the solutions are bounded. This is a joint work with Hakima
Bessaih.
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