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Volumn 42, Issue 3, 2008, Pages 375-410

Mortar finite element discretization of a model coupling Darcy and Stokes equations

Author keywords

Darcy equations; Finite elements; Mortar method; Stokes equations

Indexed keywords


EID: 42549147509     PISSN: 0764583X     EISSN: 12903841     Source Type: Journal    
DOI: 10.1051/m2an:2008009     Document Type: Article
Times cited : (58)

References (36)
  • 1
    • 0042739595 scopus 로고    scopus 로고
    • Un schéma de volumes ou éléments finis adaptatif pour les équations de Darcy à perméabilité variable.
    • Y. Achdou and C. Bernardi, Un schéma de volumes ou éléments finis adaptatif pour les équations de Darcy à perméabilité variable. C. R. Acad. Sci. Paris Sér. I 333 (2001) 693-698.
    • (2001) C. R. Acad. Sci. Paris Sér. I , vol.333 , pp. 693-698
    • Achdou, Y.1    Bernardi, C.2
  • 2
    • 0742289177 scopus 로고    scopus 로고
    • A priori and a posteriori analysis of finite volume discretizations of Darcy's equations
    • Y. Achdou, C. Bernardi and F. Coquel, A priori and a posteriori analysis of finite volume discretizations of Darcy's equations. Numer. Math. 96 (2003) 17-42.
    • (2003) Numer. Math , vol.96 , pp. 17-42
    • Achdou, Y.1    Bernardi, C.2    Coquel, F.3
  • 5
    • 0041800397 scopus 로고    scopus 로고
    • The Mortar finite element method with Lagrangian multiplier
    • F. Ben Belgacem, The Mortar finite element method with Lagrangian multiplier. Numer. Math. 84 (1999) 173-197.
    • (1999) Numer. Math , vol.84 , pp. 173-197
    • Ben Belgacem, F.1
  • 6
    • 84966261002 scopus 로고
    • Analysis of some finite elements for the Stokes problem
    • C. Bernardi and G. Raugel, Analysis of some finite elements for the Stokes problem. Math. Comput. 44 (1985) 71-79.
    • (1985) Math. Comput , vol.44 , pp. 71-79
    • Bernardi, C.1    Raugel, G.2
  • 7
    • 0002336587 scopus 로고
    • A new nonconforming approach to domain decomposition: The mortar element method
    • H. Brezis and J.-L. Lions Eds, Pitman
    • C. Bernardi, Y. Maday and A.T. Patera, A new nonconforming approach to domain decomposition: the mortar element method, in Collège de France Seminar XI, H. Brezis and J.-L. Lions Eds., Pitman (1994) 13-51.
    • (1994) Collège de France Seminar , vol.11 , pp. 13-51
    • Bernardi, C.1    Maday, Y.2    Patera, A.T.3
  • 8
    • 0347792670 scopus 로고    scopus 로고
    • Analyse numérique d'indicateurs d'erreur
    • Chap. 8, P.-L. George Ed, Hermès
    • C. Bernardi, B. Métivet and R. Verfürth, Analyse numérique d'indicateurs d'erreur, in Maillage et adaptation, Chap. 8, P.-L. George Ed., Hermès (2001) 251-278.
    • (2001) Maillage et adaptation , pp. 251-278
    • Bernardi, C.1    Métivet, B.2    Verfürth, R.3
  • 10
    • 15744389004 scopus 로고    scopus 로고
    • Coupling Darcy and Stokes equations for porous media with cracks
    • C. Bernardi, F. Hecht and O. Pironneau, Coupling Darcy and Stokes equations for porous media with cracks. ESAIM: M2AN 39 (2005) 7-35.
    • (2005) ESAIM: M2AN , vol.39 , pp. 7-35
    • Bernardi, C.1    Hecht, F.2    Pironneau, O.3
  • 12
    • 33751340055 scopus 로고    scopus 로고
    • Mortar finite element discretization for the flow in a non homogeneous porous medium
    • C. Bernardi, F. Hecht and Z. Mghazli, Mortar finite element discretization for the flow in a non homogeneous porous medium. Comput. Methods Appl. Mech. Engrg. 196 (2007) 1554-1573.
    • (2007) Comput. Methods Appl. Mech. Engrg , vol.196 , pp. 1554-1573
    • Bernardi, C.1    Hecht, F.2    Mghazli, Z.3
  • 13
    • 0001023383 scopus 로고
    • Stability of finite elements under divergence constraints
    • J. Boland and R. Nicolaides, Stability of finite elements under divergence constraints. SIAM J. Numer. Anal. 20 (1983) 722-731.
    • (1983) SIAM J. Numer. Anal , vol.20 , pp. 722-731
    • Boland, J.1    Nicolaides, R.2
  • 14
    • 0000518260 scopus 로고    scopus 로고
    • A posteriori error estimators for the Raviart-Thomas element
    • D. Braess and R. Verfürth, A posteriori error estimators for the Raviart-Thomas element. SIAM J. Numer. Anal. 33 (1996) 2431-2444.
    • (1996) SIAM J. Numer. Anal , vol.33 , pp. 2431-2444
    • Braess, D.1    Verfürth, R.2
  • 16
    • 33748428656 scopus 로고    scopus 로고
    • A unified stabilized method for Stokes' and Darcy's equations
    • E. Burman and P. Hansbo, A unified stabilized method for Stokes' and Darcy's equations. J. Comput. Applied Math. 198 (2007) 35-51.
    • (2007) J. Comput. Applied Math , vol.198 , pp. 35-51
    • Burman, E.1    Hansbo, P.2
  • 18
    • 34548090178 scopus 로고    scopus 로고
    • A unifying theory of a posteriori error control for nonconforming finite element methods
    • C. Carstensen and J. Hu, A unifying theory of a posteriori error control for nonconforming finite element methods. Numer. Math. 107 (2007) 473-502.
    • (2007) Numer. Math , vol.107 , pp. 473-502
    • Carstensen, C.1    Hu, J.2
  • 19
    • 0008276077 scopus 로고
    • Neumann and mixed problems on curvilinear polyhedra
    • M. Dauge, Neumann and mixed problems on curvilinear polyhedra. Integr. Equat. Oper. Th. 15 (1992) 227-261.
    • (1992) Integr. Equat. Oper. Th , vol.15 , pp. 227-261
    • Dauge, M.1
  • 21
    • 0036776588 scopus 로고    scopus 로고
    • Mathematical and numerical models for coupling surface and groundwater flows
    • M. Discacciati, E. Miglio and A. Quarteroni, Mathematical and numerical models for coupling surface and groundwater flows. Appl. Numer. Math. 43 (2002) 57-74.
    • (2002) Appl. Numer. Math , vol.43 , pp. 57-74
    • Discacciati, M.1    Miglio, E.2    Quarteroni, A.3
  • 22
    • 0019362553 scopus 로고
    • Old and new elements for incompressible flows
    • M. Fortin, Old and new elements for incompressible flows. Internat. J. Numer. Methods Fluids 1 (1981) 347-364.
    • (1981) Internat. J. Numer. Methods Fluids , vol.1 , pp. 347-364
    • Fortin, M.1
  • 23
    • 42549171063 scopus 로고    scopus 로고
    • Non-matching mortar discretization analysis for the coupling Stokes-Darcy equations
    • Submitted
    • J. Galvis and M. Sarkis, Non-matching mortar discretization analysis for the coupling Stokes-Darcy equations. (Submitted).
    • Galvis, J.1    Sarkis, M.2
  • 25
    • 4043060000 scopus 로고    scopus 로고
    • A domain decomposition and mixed method for a linear parabolic boundary value problem
    • V. Girault, R. Glowinski and H. López, A domain decomposition and mixed method for a linear parabolic boundary value problem. IMA J. Numer. Anal. 24 (2004) 491-520.
    • (2004) IMA J. Numer. Anal , vol.24 , pp. 491-520
    • Girault, V.1    Glowinski, R.2    López, H.3
  • 28
  • 32
    • 42549109111 scopus 로고    scopus 로고
    • M. Orlt and A.-M. Sändig, Regularity of viscous Navier-Stokes flows in nonsmooth domains, in Proc. Conf. Boundary Value Problems and Integral Equations in Nonsmooth Domains, M. Costabel, M. Dauge and S. Nicaise Eds., Lect. Notes Pure Appl. Math. 167, Dekker (1995) 185-201.
    • M. Orlt and A.-M. Sändig, Regularity of viscous Navier-Stokes flows in nonsmooth domains, in Proc. Conf. Boundary Value Problems and Integral Equations in Nonsmooth Domains, M. Costabel, M. Dauge and S. Nicaise Eds., Lect. Notes Pure Appl. Math. 167, Dekker (1995) 185-201.
  • 33
    • 33846963201 scopus 로고    scopus 로고
    • On a hierarchy of approximate models for flows of incompressible fluids through porous solids
    • K.R. Rajagopal, On a hierarchy of approximate models for flows of incompressible fluids through porous solids. Math. Models Methods Appl. Sci. 17 (2007) 215-252.
    • (2007) Math. Models Methods Appl. Sci , vol.17 , pp. 215-252
    • Rajagopal, K.R.1


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