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A mixed FEM for the coupled Brinkman–Forchheimer/Darcy problem.

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Title: A mixed FEM for the coupled Brinkman–Forchheimer/Darcy problem.
Authors: Caucao, Sergio1,2 (AUTHOR) scaucao@ucsc.cl, Discacciati, Marco3 (AUTHOR) m.discacciati@lboro.ac.uk
Source: Applied Numerical Mathematics. Aug2023, Vol. 190, p138-154. 17p.
Subjects: Lagrange multiplier, Finite element method, Conservation of mass, Porous materials, Darcy's law
Abstract: This paper develops the a priori analysis of a mixed finite element method for the filtration of an incompressible fluid through a non-deformable saturated porous medium with heterogeneous permeability. Flows are governed by the Brinkman–Forchheimer and Darcy equations in the more and less permeable regions, respectively, and the corresponding transmission conditions are given by mass conservation and continuity of momentum. We consider the standard mixed formulation in the Brinkman–Forchheimer domain and the dual-mixed one in the Darcy region, and we impose the continuity of the normal velocities by introducing suitable Lagrange multiplier. The finite element discretization involves Bernardi–Raugel and Raviart–Thomas elements for the velocities, piecewise constants for the pressures, and continuous piecewise linear elements for the Lagrange multiplier. Stability, convergence, and a priori error estimates for the associated Galerkin scheme are obtained. Numerical tests illustrate the theoretical results. [ABSTRACT FROM AUTHOR]
Copyright of Applied Numerical Mathematics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
An: 163946688
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  Data: A mixed FEM for the coupled Brinkman–Forchheimer/Darcy problem.
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  Data: <searchLink fieldCode="AR" term="%22Caucao%2C+Sergio%22">Caucao, Sergio</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> scaucao@ucsc.cl</i><br /><searchLink fieldCode="AR" term="%22Discacciati%2C+Marco%22">Discacciati, Marco</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> m.discacciati@lboro.ac.uk</i>
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  Data: <searchLink fieldCode="JN" term="%22Applied+Numerical+Mathematics%22">Applied Numerical Mathematics</searchLink>. Aug2023, Vol. 190, p138-154. 17p.
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  Data: <searchLink fieldCode="DE" term="%22Lagrange+multiplier%22">Lagrange multiplier</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+element+method%22">Finite element method</searchLink><br /><searchLink fieldCode="DE" term="%22Conservation+of+mass%22">Conservation of mass</searchLink><br /><searchLink fieldCode="DE" term="%22Porous+materials%22">Porous materials</searchLink><br /><searchLink fieldCode="DE" term="%22Darcy's+law%22">Darcy's law</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: This paper develops the a priori analysis of a mixed finite element method for the filtration of an incompressible fluid through a non-deformable saturated porous medium with heterogeneous permeability. Flows are governed by the Brinkman–Forchheimer and Darcy equations in the more and less permeable regions, respectively, and the corresponding transmission conditions are given by mass conservation and continuity of momentum. We consider the standard mixed formulation in the Brinkman–Forchheimer domain and the dual-mixed one in the Darcy region, and we impose the continuity of the normal velocities by introducing suitable Lagrange multiplier. The finite element discretization involves Bernardi–Raugel and Raviart–Thomas elements for the velocities, piecewise constants for the pressures, and continuous piecewise linear elements for the Lagrange multiplier. Stability, convergence, and a priori error estimates for the associated Galerkin scheme are obtained. Numerical tests illustrate the theoretical results. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Applied Numerical Mathematics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1016/j.apnum.2023.04.014
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 17
        StartPage: 138
    Subjects:
      – SubjectFull: Lagrange multiplier
        Type: general
      – SubjectFull: Finite element method
        Type: general
      – SubjectFull: Conservation of mass
        Type: general
      – SubjectFull: Porous materials
        Type: general
      – SubjectFull: Darcy's law
        Type: general
    Titles:
      – TitleFull: A mixed FEM for the coupled Brinkman–Forchheimer/Darcy problem.
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      – PersonEntity:
          Name:
            NameFull: Caucao, Sergio
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            NameFull: Discacciati, Marco
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          Dates:
            – D: 01
              M: 08
              Text: Aug2023
              Type: published
              Y: 2023
          Identifiers:
            – Type: issn-print
              Value: 01689274
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              Value: 190
          Titles:
            – TitleFull: Applied Numerical Mathematics
              Type: main
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