메뉴 건너뛰기




Volumn 25, Issue 2, 2009, Pages 311-326

Unified finite element discretizations of coupled darcy-stokes flow

Author keywords

Alternative weak formulations; Coupled darcy stokes flow; Nonconforming finite elements

Indexed keywords


EID: 63449104358     PISSN: 0749159X     EISSN: 10982426     Source Type: Journal    
DOI: 10.1002/num.20349     Document Type: Article
Times cited : (98)

References (23)
  • 1
    • 0002899459 scopus 로고    scopus 로고
    • Simulation of coupled viscous and porous flow problems
    • 1 D. K. Gartling, C. E. Hickox, and R. C. Givler, Simulation of coupled viscous and porous flow problems, Comp Fluid Dyn 7 (1996), 23–48.
    • (1996) Comp Fluid Dyn , vol.7 , pp. 23-48
    • Gartling, D.K.1    Hickox, C.E.2    Givler, R.C.3
  • 2
    • 0028450252 scopus 로고
    • Finite element formulations for large‐scale, coupled flows in adjacent porous and open fluid domains
    • 2 A. G. Salinger, R. Aris, and J. J. Derby, Finite element formulations for large‐scale, coupled flows in adjacent porous and open fluid domains, Int J Numer Methods Fluids 18 (1994), 1185–1209.
    • (1994) Int J Numer Methods Fluids , vol.18 , pp. 1185-1209
    • Salinger, A.G.1    Aris, R.2    Derby, J.J.3
  • 3
    • 0347337976 scopus 로고    scopus 로고
    • Coupling fluid flow with porous media flow
    • 3 W. Layton, F. Schieweck, and I. Yotov, Coupling fluid flow with porous media flow, SIAM J Numer Anal 40 (2003), 2195–2218.
    • (2003) SIAM J Numer Anal , vol.40 , pp. 2195-2218
    • Layton, W.1    Schieweck, F.2    Yotov, I.3
  • 4
    • 0036776588 scopus 로고    scopus 로고
    • Mathematical and numerical models for coupling surface and groundwater flows
    • 4 E. Miglio, M. Discacciati, 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
    • Miglio, E.1    Discacciati, M.2    Quarteroni, A.3
  • 5
    • 85120593328 scopus 로고    scopus 로고
    • A conforming mixed finite element method for the coupling of fluid flow with porous media flow, Preprint 06‐01, Departamento de Ingeniería Mathemática
    • 5 G. Gatica, S. Meddahi, and R. Oyarzúa, A conforming mixed finite element method for the coupling of fluid flow with porous media flow, Preprint 06‐01, Departamento de Ingeniería Mathemática, Universidad de Concepción, 2006.
    • (2006)
    • Gatica, G.1    Meddahi, S.2    Oyarzúa, R.3
  • 6
    • 17444430004 scopus 로고    scopus 로고
    • Analysis of a discontinuous finite element method for the coupled Stokes and Darcy problem
    • 6 B. Rivière, Analysis of a discontinuous finite element method for the coupled Stokes and Darcy problem, J Sci Comput 22 (2005), 479–500.
    • (2005) J Sci Comput , vol.22 , pp. 479-500
    • Rivière, B.1
  • 7
    • 27744551448 scopus 로고    scopus 로고
    • Locally conservative coupling of Stokes and Darcy flows
    • 7 B. Rivière and I. Yotov, Locally conservative coupling of Stokes and Darcy flows, SIAM J Numer Anal 42 (2005), 1959–1977.
    • (2005) SIAM J Numer Anal , vol.42 , pp. 1959-1977
    • Rivière, B.1    Yotov, I.2
  • 8
    • 85028182647 scopus 로고    scopus 로고
    • A computational method for approximating a Darcy‐Stokes system governing a vuggy porous medium, ICES Report 03–47
    • 8 T. Arbogast and D. S. Brunson, A computational method for approximating a Darcy‐Stokes system governing a vuggy porous medium, ICES Report 03–47, University of Texas, Austin, 2003.
    • (2003)
    • Arbogast, T.1    Brunson, D.S.2
  • 9
    • 0019362553 scopus 로고
    • Old and new finite elements for incompressible flows
    • 9 M. Fortin, Old and new finite elements for incompressible flows, Int J Numer Methods Fluids 1 (1981), 347–364.
    • (1981) Int J Numer Methods Fluids , vol.1 , pp. 347-364
    • Fortin, M.1
  • 10
    • 27744482072 scopus 로고    scopus 로고
    • A family of rectangular mixed elements with a continuous flux for second order elliptic problems
    • 10 T. Arbogast and M. Wheeler, A family of rectangular mixed elements with a continuous flux for second order elliptic problems, SIAM J Numer Anal 42 (2005), 1914–1931.
    • (2005) SIAM J Numer Anal , vol.42 , pp. 1914-1931
    • Arbogast, T.1    Wheeler, M.2
  • 11
    • 78149488189 scopus 로고
    • Boundary conditions at a natural permeable wall
    • 11 G. S. Beavers and D. D. Joseph, Boundary conditions at a natural permeable wall, J Fluid Mech 30 (1967), 197–207.
    • (1967) J Fluid Mech , vol.30 , pp. 197-207
    • Beavers, G.S.1    Joseph, D.D.2
  • 12
    • 0042826384 scopus 로고
    • On the boundary conditions at the interface of a porous medium
    • 12 P. G. Saffmann, On the boundary conditions at the interface of a porous medium, Studies Appl Math 1 (1973), 93–101.
    • (1973) Studies Appl Math , vol.1 , pp. 93-101
    • Saffmann, P.G.1
  • 13
    • 0344896697 scopus 로고    scopus 로고
    • A robust finite element method for the Darcy‐Stokes flow
    • 13 K.‐A. Mardal, X.‐C. Tai, and R. Winther, A robust finite element method for the Darcy‐Stokes flow, SIAM J Numer Anal 40 (2002), 1605–1631.
    • (2002) SIAM J Numer Anal , vol.40 , pp. 1605-1631
    • Mardal, K.‐A.1    Tai, X.‐C.2    Winther, R.3
  • 14
    • 33846372237 scopus 로고    scopus 로고
    • A discrete de Rahm complex with enhanced smoothness
    • 14 X.‐C. Tai and R. Winther, A discrete de Rahm complex with enhanced smoothness, Calcolo 43 (2006), 287–306.
    • (2006) Calcolo , vol.43 , pp. 287-306
    • Tai, X.‐C.1    Winther, R.2
  • 15
    • 0016093926 scopus 로고
    • On the existence, uniqueness and approximation of saddle‐point problems arising from Lagrangian multipliers
    • 15 F. Brezzi, On the existence, uniqueness and approximation of saddle‐point problems arising from Lagrangian multipliers, RAIRO Numer Anal 8 (1974), 129–151.
    • (1974) RAIRO Numer Anal , vol.8 , pp. 129-151
    • Brezzi, F.1
  • 16
    • 2942670777 scopus 로고    scopus 로고
    • Korn's inequalities for picewise H1 vector fields
    • 16 S. Brenner, Korn's inequalities for picewise H 1 vector fields, Math Comput 73 (2003), 1067–1087.
    • (2003) Math Comput , vol.73 , pp. 1067-1087
    • Brenner, S.1
  • 17
    • 0003507785 scopus 로고
    • Finite element methods for Navier Stokes equations
    • 17 V. Girault and P.‐A. Raviart, Finite element methods for Navier Stokes equations, Springer, 1986.
    • (1986)
    • Girault, V.1    Raviart, P.‐A.2
  • 18
    • 1842459324 scopus 로고    scopus 로고
    • Poincaré–Friedrichs inequalities for piecewise H1 functions
    • 18 S. Brenner, Poincaré–Friedrichs inequalities for piecewise H 1 functions, SIAM J Numer Anal 41 (2003), 306–324.
    • (2003) SIAM J Numer Anal , vol.41 , pp. 306-324
    • Brenner, S.1
  • 19
    • 32944468762 scopus 로고    scopus 로고
    • An observation on Korn's inequality for nonconforming finite element methods
    • 19 K.‐A. Mardal and R. Winther, An observation on Korn's inequality for nonconforming finite element methods, Math Comput 75 (2006), 1–6.
    • (2006) Math Comput , vol.75 , pp. 1-6
    • Mardal, K.‐A.1    Winther, R.2
  • 20
    • 51249186403 scopus 로고
    • A stable finite element for the Stokes equation
    • 20 D. N. Arnold, F. Brezzi, and M. Fortin, A stable finite element for the Stokes equation, Calcolo 21 (1984), 337–344.
    • (1984) Calcolo , vol.21 , pp. 337-344
    • Arnold, D.N.1    Brezzi, F.2    Fortin, M.3
  • 21
    • 0003966593 scopus 로고    scopus 로고
    • Finite elements—Fast solvers and applications in solid mechanics
    • 21 D. Braess, Finite elements—Fast solvers and applications in solid mechanics, 2nd Ed., Cambridge University Press, 2001.
    • (2001)
    • Braess, D.1
  • 22
    • 0016541865 scopus 로고
    • Approximation by finite element functions using local regularizations
    • 22 P. Clement, Approximation by finite element functions using local regularizations, RAIRO Numer Anal 9 (1975), 77–84.
    • (1975) RAIRO Numer Anal , vol.9 , pp. 77-84
    • Clement, P.1
  • 23
    • 0003881705 scopus 로고
    • Mixed and hybrid finite element methods
    • 23 F. Brezzi and M. Fortin, Mixed and hybrid finite element methods, Springer, 1991.
    • (1991)
    • Brezzi, F.1    Fortin, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.