000218097 001__ 218097
000218097 005__ 20190317000427.0
000218097 0247_ $$2doi$$a10.1016/j.cma.2016.10.008
000218097 022__ $$a0045-7825
000218097 02470 $$2ISI$$a000390740900021
000218097 037__ $$aARTICLE
000218097 245__ $$aA posteriori error estimation for the steady Navier-Stokes equations in random domains
000218097 260__ $$bElsevier$$c2017$$aLausanne
000218097 269__ $$a2017
000218097 300__ $$a29
000218097 336__ $$aJournal Articles
000218097 520__ $$aWe 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.
000218097 6531_ $$aa posteriori error estimate
000218097 6531_ $$aFinite element method
000218097 6531_ $$aUncertainty quantification
000218097 6531_ $$aRandom domains
000218097 6531_ $$aNavier-Stokes equations
000218097 700__ $$0246820$$g175859$$aGuignard, Diane Sylvie
000218097 700__ $$0241873$$g118353$$aNobile, Fabio
000218097 700__ $$0241282$$g106096$$aPicasso, Marco
000218097 773__ $$j313$$tComputer Methods in Applied Mechanics and Engineering$$q483-511
000218097 787__ $$eIs New Version Of$$whttps://infoscience.epfl.ch/record/263555
000218097 8564_ $$uhttps://infoscience.epfl.ch/record/218097/files/2017_Guignard_Nobile_Picasso_CMAME_NavierStokes.pdf$$zPublisher's version$$s968138$$yPublisher's version
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000218097 909C0 $$pASN$$xU10795$$0252201
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000218097 917Z8 $$x178574
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000218097 937__ $$aEPFL-ARTICLE-218097
000218097 973__ $$rREVIEWED$$sPUBLISHED$$aEPFL
000218097 980__ $$aARTICLE