Stochastic Galerkin methods for the steady-state Navier-Stokes equations

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1506.08899.pdf (1.8 MB)

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https://arxiv.org/abs/1506.08899

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http://hdl.handle.net/11603/23156

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UMBC Mathematics and Statistics Department
UMBC Faculty Collection

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https://orcid.org/0000-0002-8053-8956

Date

2016-04-14

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journal articles
preprints
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Citation of Original Publication

Sousedík, Bedřich; Elman, Howard C.; Stochastic Galerkin methods for the steady-state Navier-Stokes equations; Journal of Computational Physics, 316, 435-452

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Abstract

We study the steady-state Navier-Stokes equations in the context of stochastic finite element discretizations. Specifically, we assume that the viscosity is a random field given in the form of a generalized polynomial chaos expansion. For the resulting stochastic problem, we formulate the model and linearization schemes using Picard and Newton iterations in the framework of the stochastic Galerkin method, and we explore properties of the resulting stochastic solutions. We also propose a preconditioner for solving the linear systems of equations arising at each step of the stochastic (Galerkin) nonlinear iteration and demonstrate its effectiveness for solving a set of benchmark problems.