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A posteriori error analysis for Navier–Stokes equations coupled with Darcy problem

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Abstract

Our aim in this paper is to study the interaction between surface and subsurface flows. The model considered is a system coupling Navier–Stokes and Darcy equations. We make use of a discontinuous Galerkin finite element method for the discretisation of this problem. Then we develop a posteriori error analysis for the resulting discrete problem. Numerical experimentations confirm our analytical results.

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Acknowledgments

This work was supported by the Algerian National Project PNR 08/23/977. The authors are thankful and grateful to the referees for their fruitful remarks, comments and suggestions.

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Authors and Affiliations

  1. Probability and Statistics Laboratory (LAPS), Department of Mathematics, Faculty of Sciences, PO Box 12, 23000, Annaba, Algeria

    M. L. Hadji

  2. Mathematical Modeling and Numerical Simulation Laboratory, Department of Mathematics, Faculty of Sciences, Badji-Mokhtar University, PO Box. 12, 23000, Annaba, Algeria

    A. Assala & F. Z. Nouri

Authors
  1. M. L. Hadji
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  2. A. Assala
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  3. F. Z. Nouri
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Correspondence to F. Z. Nouri.

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Hadji, M.L., Assala, A. & Nouri, F.Z. A posteriori error analysis for Navier–Stokes equations coupled with Darcy problem. Calcolo 52, 559–576 (2015). https://doi.org/10.1007/s10092-014-0130-z

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  • DOI: https://doi.org/10.1007/s10092-014-0130-z

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