Abstract:
In this paper we develop and analyze a unified approximation of the velocity–pressure pair for the Stokes–Darcy coupled problem in a plane domain. It is well known that, stable finite element approximations for the Stokes problem may not be appropriate for Darcy problem and for the coupling of fluid flow (modeled by the Stokes equations) with porous media flow (modeled by the Darcy equation), and therefore, different spaces are commonly used for the discretizations of the Darcy and the Stokes problems. In this work we proposed a modification of the Darcy problem which allows us to apply the classical Mini-element to the whole coupled Stokes–Darcy problem. The proposed method is probably one of the cheapest method for continuous approximation of the coupled system, has optimal accuracy with respect to solution regularity, and has simple and straightforward implementations. Numerical experiments are also presented, which confirm the excellent stability and accuracy of our method. © 2018 Elsevier Ltd
Registro:
Documento: |
Artículo
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Título: | A unified mixed finite element approximations of the Stokes–Darcy coupled problem |
Autor: | Armentano, M.G.; Stockdale, M.L. |
Filiación: | Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, 1428, Argentina; IMAS - Conicet, Buenos Aires, 1428, Argentina
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Palabras clave: | Mixed finite elements; Stability analysis; Stokes–Darcy problem; Finite element method; Navier Stokes equations; Numerical methods; Porous materials; Continuous approximations; Finite element approximations; Mixed finite element approximation; Mixed finite elements; Numerical experiments; Optimal accuracy; Porous-media flow; Stability analysis; Flow of fluids |
Año: | 2019
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Volumen: | 77
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Número: | 9
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Página de inicio: | 2568
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Página de fin: | 2584
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DOI: |
http://dx.doi.org/10.1016/j.camwa.2018.12.032 |
Título revista: | Computers and Mathematics with Applications
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Título revista abreviado: | Comput Math Appl
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ISSN: | 08981221
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CODEN: | CMAPD
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_08981221_v77_n9_p2568_Armentano |
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Citas:
---------- APA ----------
Armentano, M.G. & Stockdale, M.L.
(2019)
. A unified mixed finite element approximations of the Stokes–Darcy coupled problem. Computers and Mathematics with Applications, 77(9), 2568-2584.
http://dx.doi.org/10.1016/j.camwa.2018.12.032---------- CHICAGO ----------
Armentano, M.G., Stockdale, M.L.
"A unified mixed finite element approximations of the Stokes–Darcy coupled problem"
. Computers and Mathematics with Applications 77, no. 9
(2019) : 2568-2584.
http://dx.doi.org/10.1016/j.camwa.2018.12.032---------- MLA ----------
Armentano, M.G., Stockdale, M.L.
"A unified mixed finite element approximations of the Stokes–Darcy coupled problem"
. Computers and Mathematics with Applications, vol. 77, no. 9, 2019, pp. 2568-2584.
http://dx.doi.org/10.1016/j.camwa.2018.12.032---------- VANCOUVER ----------
Armentano, M.G., Stockdale, M.L. A unified mixed finite element approximations of the Stokes–Darcy coupled problem. Comput Math Appl. 2019;77(9):2568-2584.
http://dx.doi.org/10.1016/j.camwa.2018.12.032