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Stochastic Steady-State Navier–Stokes Equations with Additive Random Noise

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Abstract

In this paper we investigate mathematically and numerically the two-dimensional stochastic steady-state incompressible Navier–Stokes equations with an additive random noise represented by a series in terms of truncated standard normal random variables and orthogonal basis functions. The existence and uniqueness of solutions are established. A statistical error estimate for the finite element methods is derived. A computational approach involving eigen-bases for a stochastic elliptic system is discussed and results of numerical tests are presented to validate the method.

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Acknowledgments

Max Gunzburger supported in part by the US Department of Energy Office of Science under grant number DE-SC0010678.

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Author notes

  1. Ju Ming

    Present address: Beijing Computational Science Research Center, 3 Heqing Road, Beijing, 100084, China

Authors and Affiliations

  1. Department of Scientific Computing, Florida State University, Tallahassee, FL, 32306, USA

    Max D. Gunzburger & Ju Ming

  2. Department of Mathematics, Iowa State University, Ames, IA, 50010, USA

    Lisheng Hou

Authors
  1. Max D. Gunzburger
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  2. Lisheng Hou
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  3. Ju Ming
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Correspondence to Lisheng Hou.

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Gunzburger, M.D., Hou, L. & Ming, J. Stochastic Steady-State Navier–Stokes Equations with Additive Random Noise. J Sci Comput 66, 672–691 (2016). https://doi.org/10.1007/s10915-015-0039-y

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  • DOI: https://doi.org/10.1007/s10915-015-0039-y

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