218097
20190317000427.0
0045-7825
10.1016/j.cma.2016.10.008
doi
000390740900021
ISI
ARTICLE
A posteriori error estimation for the steady Navier-Stokes equations in random domains
Lausanne
2017
Elsevier
2017
29
Journal Articles
We consider finite element error approximations of the steady incompressible Navier-Stokes equations defined on a randomly perturbed domain, the perturbation being small. Introducing a random mapping, these equations are transformed into PDEs on a fixed reference domain with random coefficients. Under suitable assumptions on the random mapping and the input data, in particular the so-called small data assumption, we prove the well-posedness of the problem. We assume then that the mapping depends affinely on L independent random variables and adopt a perturbation approach expanding the solution with respect to a small parameter ε that controls the amount of randomness in the problem. We perform an a posteriori error analysis for the first order approximation error, namely the error between the exact (random) solution and the finite element approximation of the first term in the expansion with respect to ε. Numerical results are given to illustrate the theoretical results and the effectiveness of the error estimators.
a posteriori error estimate
Finite element method
Uncertainty quantification
Random domains
Navier-Stokes equations
Guignard, Diane Sylvie
175859
246820
Nobile, Fabio
118353
241873
Picasso, Marco
106096
241282
483-511
Computer Methods in Applied Mechanics and Engineering
313
Is New Version Of
https://infoscience.epfl.ch/record/263555
Publisher's version
968138
Publisher's version
http://infoscience.epfl.ch/record/218097/files/2017_Guignard_Nobile_Picasso_CMAME_NavierStokes.pdf
CSQI
252411
U12495
ASN
252201
U10795
oai:infoscience.tind.io:218097
article
SB
GLOBAL_SET
178574
178574
175859
118353
EPFL-ARTICLE-218097
EPFL
PUBLISHED
REVIEWED
ARTICLE