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Time-discretization of stochastic 2-D Navier–Stokes equations with a penalty-projection method

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Abstract

A time-discretization of the stochastic incompressible Navier–Stokes problem by penalty method is analyzed. Some error estimates are derived, combined, and eventually arrive at a speed of convergence in probability of order 1/4 of the main algorithm for the pair of variables velocity and pressure. Also, using the law of total probability, we obtain the strong convergence of the scheme for both variables.

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Authors and Affiliations

  1. Lehrstuhl Angewandte Mathematik, Montanuniversität Leoben, Peter-Tunner-Straße 25-27, 8700, Leoben, Austria

    Erika Hausenblas

  2. Fakultät für Mathematik, Universität Bielefeld, Universitätsstraße 25, 33615, Bielefeld, Germany

    Tsiry A. Randrianasolo

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  1. Erika Hausenblas
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  2. Tsiry A. Randrianasolo
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Correspondence to Tsiry A. Randrianasolo.

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The authors would like to thank M. Hutzenthaler and P.A. Razafimandimby for stimulating discussions. They are also grateful to the referee for his comments and suggestions which helped to improve the presentation of the paper. This work was part of the second author’s Ph.D. Dissertation at Montanuniversität Leoben and was supported by the Austrian Science Fund (FWF): P26958 and the German Research Foundation as part of the Collaborative Research Center SFB 1283.

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Hausenblas, E., Randrianasolo, T.A. Time-discretization of stochastic 2-D Navier–Stokes equations with a penalty-projection method. Numer. Math. 143, 339–378 (2019). https://doi.org/10.1007/s00211-019-01057-3

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  • DOI: https://doi.org/10.1007/s00211-019-01057-3

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