Oberseminar AG Mathematische Modellierung

Montag, den 05. Juni 2023 um 17.00 Uhr, in B7-209 Seminarraum A

Vortrag von Prof. Dr. Dominic Breit (Clausthal) mit dem Titel: "Error analysis for 2D stochastic Navier– Stokes equations in bounded domains"

 

Abstrakt: 

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) 1/2in time and 1 in space. This was previously only known in the space-periodic case, where higher order energy estimates for any given (deterministic) time are available. 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) from earlier contributions. This is a joint work with Andreas Prohl.