Numerical approximation of the 2D stochastic Navier--Stokes equations: Dirichlet case
A talk in the BI.discrete series by
Dominic Breit from TU Clausthal
| Abstract: | We study a finite-element based space-time discretisation for the 2D stochastic Navier--Stokes equations in a bounded domain supplemented with no-slip boundary conditions. We prove optimal convergence rates in the energy norm with respect to convergence in probability, that is convergence of order (almost) 1/2 in time and 1 in space. In the space-periodic case a corresponding result hinges on higher order energy estimates for any given (deterministic) time. In contrast to this, in the Dirichlet-case estimates are only known for a (possibly large) stopping time. We overcome this problem by introducing an approach based on discrete stopping times. This replaces the localised estimates (with respect to the sample space) used in the periodic case.
For additive noise we obtain convergence rate in time. This is based on the transformation to a random PDE.
Zoom Meeting ID: [926 5310 0938] Passcode: [1928 $\href{https://uni-bielefeld.zoom.us/j/92653100938?pwd=QjB6MS95RU9PMXJWcXZpcjV0OG5NZz09}{\textbf{Join Zoom Meeting}}$ Within the CRC this talk is associated to the project(s): B7 |