42,127 research outputs found
Parameter Estimation for the Stochastically Perturbed Navier-Stokes Equations
We consider a parameter estimation problem to determine the viscosity
of a stochastically perturbed 2D Navier-Stokes system. We derive several
different classes of estimators based on the first Fourier modes of a
single sample path observed on a finite time interval. We study the consistency
and asymptotic normality of these estimators. Our analysis treats strong,
pathwise solutions for both the periodic and bounded domain cases in the
presence of an additive white (in time) noise.Comment: to appear in SP
A weighted reduced basis method for parabolic PDEs with random data
This work considers a weighted POD-greedy method to estimate statistical
outputs parabolic PDE problems with parametrized random data. The key idea of
weighted reduced basis methods is to weight the parameter-dependent error
estimate according to a probability measure in the set-up of the reduced space.
The error of stochastic finite element solutions is usually measured in a root
mean square sense regarding their dependence on the stochastic input
parameters. An orthogonal projection of a snapshot set onto a corresponding POD
basis defines an optimum reduced approximation in terms of a Monte Carlo
discretization of the root mean square error. The errors of a weighted
POD-greedy Galerkin solution are compared against an orthogonal projection of
the underlying snapshots onto a POD basis for a numerical example involving
thermal conduction. In particular, it is assessed whether a weighted POD-greedy
solutions is able to come significantly closer to the optimum than a
non-weighted equivalent. Additionally, the performance of a weighted POD-greedy
Galerkin solution is considered with respect to the mean absolute error of an
adjoint-corrected functional of the reduced solution.Comment: 15 pages, 4 figure
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