Guignard, Diane Sylvie
Nobile, Fabio
Picasso, Marco
A posteriori error estimation for the steady Navier-Stokes equations in random domains
Computer Methods in Applied Mechanics and Engineering
0045-7825
10.1016/j.cma.2016.10.008
313
483-511
29
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;
Elsevier
Lausanne
2017
http://infoscience.epfl.ch/record/218097/files/2017_Guignard_Nobile_Picasso_CMAME_NavierStokes.pdf;