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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