A posteriori error estimates for the time-dependent convection-diffusion-reaction equation coupled with the Darcy system | Numerical Algorithms
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A posteriori error estimates for the time-dependent convection-diffusion-reaction equation coupled with the Darcy system

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Abstract

In this article, we consider the time-dependent convection-diffusion-reaction equation coupled with the Darcy equation. We propose a numerical scheme based on finite element methods for the discretization in space and the implicit Euler method for the discretization in time. We establish optimal a posteriori error estimates with two types of computable error indicators, the first one linked to the time discretization and the second one to the space discretization. Finally, numerical investigations are performed and presented.

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Authors and Affiliations

  1. Laboratoire de Mathématiques et Applications, Unité de recherche Mathématiques et Modélisation, CAR, Faculté des Sciences, Université Saint-Joseph, B.P 11-514 Riad El Solh, Beirut, 1107 2050, Lebanon

    Nancy Chalhoub, Toni Sayah & Rebecca El Zahlaniyeh

  2. Laboratoire de Géométrie, Analyse et Applications, LAGA, CNRS, UMR 7539, Université Sorbonne Paris Nord, F-93430, Villetaneuse, France

    Pascal Omnes & Rebecca El Zahlaniyeh

  3. DES-Service de thermohydraulique et de mécanique des fluides (STMF), CEA, Université Paris-Saclay, F-91191, Gif-sur-Yvette, France

    Pascal Omnes

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  1. Nancy Chalhoub
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  2. Pascal Omnes
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  3. Toni Sayah
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  4. Rebecca El Zahlaniyeh
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Correspondence to Rebecca El Zahlaniyeh.

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Chalhoub, N., Omnes, P., Sayah, T. et al. A posteriori error estimates for the time-dependent convection-diffusion-reaction equation coupled with the Darcy system. Numer Algor 89, 1247–1286 (2022). https://doi.org/10.1007/s11075-021-01152-3

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  • DOI: https://doi.org/10.1007/s11075-021-01152-3

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