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A posteriori error analysis of the time dependent Navier–Stokes equations with mixed boundary conditions

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Abstract

In this paper we study the time dependent Navier–Stokes problem with mixed boundary conditions. The problem is discretized by the backward Euler’s scheme in time and finite elements in space. We establish optimal a posteriori error estimates with two types of computable error indicators, the first one being linked to the time discretization and the second one to the space discretization. We finish with numerical validation experiments.

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Authors and Affiliations

  1. Laboratoire Jacques-Louis Lions, C.N.R.S. and Université Pierre et Marie Curie, B.C. 187, 4 place Jussieu, 75252, Paris Cedex 05, France

    Christine Bernardi

  2. Faculté des Sciences, Université Saint-Joseph, B.P 11-514 , Riad El Solh, Beyrouth, 1107 2050, Lebanon

    Toni Sayah

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  1. Christine Bernardi
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  2. Toni Sayah
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Correspondence to Christine Bernardi.

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Bernardi, C., Sayah, T. A posteriori error analysis of the time dependent Navier–Stokes equations with mixed boundary conditions. SeMA 69, 1–23 (2015). https://doi.org/10.1007/s40324-015-0033-1

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  • DOI: https://doi.org/10.1007/s40324-015-0033-1

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