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Tuesday, June 9, 2020 - 14:15 in ZOOM - Video Conference


Convergence rates for the numerical approximation of the 2D stochastic Navier-Stokes equations

A talk in the Oberseminar Numerik series by
Dominic Breit

Abstract: ID 926 5310 0938, Password 1928 We study the stochastic Navier-Stokes equations in two dimensions with respect to periodic boundary conditions. The equations are perturbed by a nonlinear multiplicative stochastic forcing with linear growth (in the velocity) driven by a cylindrical Wiener process. We establish convergence rates for a finite-element based space-time approximation with respect to convergence in probability (where the error is measure in the energy norm). Our main result provides linear convergence in space and convergence of order (almost) 1/2 in time. This improves earlier results by Carelli-Prohl, where the convergence rate in time is only (almost) 1/4. Our approach is based on a careful analysis of the pressure function using a stochastic pressure decomposition.



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