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Volumn 16, Issue C, 2011, Pages 1-209

Numerical Methods for Grade-Two Fluid Models. Finite-Element Discretizations and Algorithms

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EID: 78650722943     PISSN: 15708659     EISSN: None     Source Type: Book Series    
DOI: 10.1016/B978-0-444-53047-9.00001-0     Document Type: Chapter
Times cited : (5)

References (109)
  • 1
    • 62549113841 scopus 로고    scopus 로고
    • Upwind discretization of a time-dependent two-dimensional grade-two fluid model
    • Abboud H. Sayah T. Upwind discretization of a time-dependent two-dimensional grade-two fluid model Comp. Math. Appl. 57 8 2009 1249-1264
    • (2009) Comp. Math. Appl , vol.57 , Issue.8 , pp. 1249-1264
    • Abboud, H.1    Sayah, T.2
  • 2
  • 4
    • 7544243351 scopus 로고    scopus 로고
    • Transport equations and Cauchy problems for BV vector fields
    • Ambrosio L. Transport equations and Cauchy problems for BV vector fields Invent. Math. 158 2004 227-260
    • (2004) Invent. Math. , vol.158 , pp. 227-260
    • Ambrosio, L.1
  • 5
    • 0032097489 scopus 로고    scopus 로고
    • Vector potentials in three-dimensional non-smooth domains Math
    • Amrouche C. Bernardi C. Dauge M. Girault V. Vector potentials in three-dimensional non-smooth domains Math. Methods Appl. Sci. 21 1998 823-864
    • (1998) Methods Appl. Sci , vol.21 , pp. 823-864
    • Amrouche, C.1    Bernardi, C.2    Dauge, M.3    Girault, V.4
  • 6
    • 51249186403 scopus 로고
    • A stable finite element for the Stokes equations
    • Arnold D. Brezzi F. Fortin M. A stable finite element for the Stokes equations Calcolo 21 4 1984 337-344
    • (1984) Calcolo , vol.21 , Issue.4 , pp. 337-344
    • Arnold, D.1    Brezzi, F.2    Fortin, M.3
  • 7
    • 34250459417 scopus 로고
    • The finite element method with Lagrangian multipliers
    • Babuška I. The finite element method with Lagrangian multipliers Numer. Math. 20 1973 179-192
    • (1973) Numer. Math. , vol.20 , pp. 179-192
    • Babuška, I.1
  • 8
    • 0000469206 scopus 로고
    • Problèmes aux limites pour leséquations aux dérivées partielles du premier ordre à coefficients réels; Théorèmes d'approximation; Application à l'équation de transport
    • Bardos C. Problèmes aux limites pour leséquations aux dérivées partielles du premier ordre à coefficients réels; Théorèmes d'approximation; Application à l'équation de transport Ann. Scient. Éc. Norm. Sup., Série 4 3 1970 185-233
    • (1970) Ann. Scient. Éc. Norm. Sup., Série , vol.4 , Issue.3 , pp. 185-233
    • Bardos, C.1
  • 9
    • 0012744759 scopus 로고
    • Existence results in Sobolev spaces for a stationary transport equation
    • Beirão Da Veiga H. Existence results in Sobolev spaces for a stationary transport equation Ricerche di Matematica Suppl. 36 1987 173-184
    • (1987) Ricerche di Matematica Suppl , vol.36 , pp. 173-184
    • Beirão Da Veiga, H.1
  • 10
    • 0003385001 scopus 로고
    • Error estimates for finite element method solution of the Stokes problem in the primitive variables
    • Bercovier M. Pironneau O. Error estimates for finite element method solution of the Stokes problem in the primitive variables Numer. Math. 33 1979 211-224
    • (1979) Numer. Math. , vol.33 , pp. 211-224
    • Bercovier, M.1    Pironneau, O.2
  • 12
    • 0032686188 scopus 로고    scopus 로고
    • Stationary problem of second-grade fluids in three dimensions: existence, uniqueness and regularity
    • Bernard J.M. Stationary problem of second-grade fluids in three dimensions: existence, uniqueness and regularity Math. Methods Appl. Sci. 22 1999 655-687
    • (1999) Math. Methods Appl. Sci. , vol.22 , pp. 655-687
    • Bernard, J.M.1
  • 13
    • 0000347589 scopus 로고
    • Optimal finite element interpolation on curved domains
    • Bernardi C. Optimal finite element interpolation on curved domains SIAM J. Numer. Anal. 26 1989 1212-1240
    • (1989) SIAM J. Numer. Anal. , vol.26 , pp. 1212-1240
    • Bernardi, C.1
  • 14
    • 0001625423 scopus 로고    scopus 로고
    • A local regularization operator for triangular and quadrilateral finite elements
    • Bernardi C. Girault V. A local regularization operator for triangular and quadrilateral finite elements SIAM J. Numer. Anal. 35 5 1998 1893-1916
    • (1998) SIAM J. Numer. Anal. , vol.35 , Issue.5 , pp. 1893-1916
    • Bernardi, C.1    Girault, V.2
  • 15
    • 84966261002 scopus 로고
    • Analysis of some finite elements for the Stokes problem
    • Bernardi C. Raugel G. Analysis of some finite elements for the Stokes problem Math. Comp. 44 169 1985 71-79
    • (1985) Math. Comp. , vol.44 , Issue.169 , pp. 71-79
    • Bernardi, C.1    Raugel, G.2
  • 16
    • 0001023383 scopus 로고
    • Stablility of finite elements under divergence constraints
    • Boland J. Nicolaides R. Stablility of finite elements under divergence constraints SIAM J. Numer. Anal. 20 4 1983 722-731
    • (1983) SIAM J. Numer. Anal. , vol.20 , Issue.4 , pp. 722-731
    • Boland, J.1    Nicolaides, R.2
  • 18
    • 78650718504 scopus 로고    scopus 로고
    • On the existence of solutions for nonstationary second-grade fluids
    • Ammann H., VSP/TEV, Vilnius Lithuania 15-30
    • Bresch D. Lemoine J. On the existence of solutions for nonstationary second-grade fluids Navier-Stokes Equations and Related Nonlinear Problems 1998 Ammann H., VSP/TEV, Vilnius Lithuania 15-30
    • (1998) Navier-Stokes Equations and Related Nonlinear Problems
    • Bresch, D.1    Lemoine, J.2
  • 19
    • 0016093926 scopus 로고
    • On the existence, uniqueness and approximation of saddlepoint problems arising from Lagrange multipliers
    • Brezzi F. On the existence, uniqueness and approximation of saddlepoint problems arising from Lagrange multipliers RAIRO, Anal. Num. R2 1974 129-151
    • (1974) RAIRO, Anal. Num. , vol.R2 , pp. 129-151
    • Brezzi, F.1
  • 21
    • 11244255133 scopus 로고    scopus 로고
    • Discontinuous Galerkin methods for first-order hyperbolic problems
    • Brezzi F. Marini L.D. Süli E. Discontinuous Galerkin methods for first-order hyperbolic problems Math. Mod. Methods Appl. Sci. 14 2004 1893-1903
    • (2004) Math. Mod. Methods Appl. Sci. , vol.14 , pp. 1893-1903
    • Brezzi, F.1    Marini, L.D.2    Süli, E.3
  • 22
    • 78650730896 scopus 로고    scopus 로고
    • Private oral communication
    • Chacón-Rebollo T. Private oral communication 2001
    • (2001)
    • Chacón-Rebollo, T.1
  • 24
    • 8544220284 scopus 로고
    • Basic error estimates for elliptic problems
    • Ciarlet P.G. Lions J.L., Finite Element Methods, Part 1 Elsevier North-Holland, Amsterdam
    • Ciarlet P.G. Basic error estimates for elliptic problems Handbook of Numerical Analysis Ciarlet P.G. Lions J.L., Finite Element Methods, Part 1 Elsevier North-Holland, Amsterdam 1991
    • (1991) Handbook of Numerical Analysis
    • Ciarlet, P.G.1
  • 25
    • 0031104128 scopus 로고    scopus 로고
    • Weak and classical solutions of a family of second grade fluids
    • Cioranescu D. Girault V. Weak and classical solutions of a family of second grade fluids Int. J. Non Linear Mech. 32 1997 317-335
    • (1997) Int. J. Non Linear Mech. , vol.32 , pp. 317-335
    • Cioranescu, D.1    Girault, V.2
  • 26
    • 77956841396 scopus 로고    scopus 로고
    • Some theoretical and numerical aspects of grade-two fluid models
    • Jaeger W. Nečas J. John O. Najzar K. Stara J. Research Notes in Mathematics 406 Chapman ' Hall/CRC New York, NY
    • Cioranescu D. Girault V. Glowinski R. Scott L.R. Some theoretical and numerical aspects of grade-two fluid models Partial Differential Equations-Theory and Numerical Solution Jaeger W. Nečas J. John O. Najzar K. Stara J. Research Notes in Mathematics 406 Chapman ' Hall/CRC New York, NY 99-110 1999
    • (1999) Partial Differential Equations-Theory and Numerical Solution , pp. 99-110
    • Cioranescu, D.1    Girault, V.2    Glowinski, R.3    Scott, L.R.4
  • 27
    • 0001398698 scopus 로고
    • Existence et unicité pour les fluids de second grade
    • Série I
    • Cioranescu D. Ouazar E.H. Existence et unicité pour les fluids de second grade C. R. Acad. Sci. Paris 298 Série I 1984 285-287
    • (1984) C. R. Acad. Sci. Paris , vol.298 , pp. 285-287
    • Cioranescu, D.1    Ouazar, E.H.2
  • 28
    • 0001452720 scopus 로고
    • Existence and uniqueness for fluids of second grade
    • Collège de France Seminar Pitman 109 Boston, MA
    • Cioranescu D. Ouazar E.H. Existence and uniqueness for fluids of second grade Nonlinear Partial Differential Equations 1984 Collège de France Seminar Pitman 109 Boston, MA 178-197
    • (1984) Nonlinear Partial Differential Equations , pp. 178-197
    • Cioranescu, D.1    Ouazar, E.H.2
  • 29
    • 0016541865 scopus 로고
    • Approximation by finite element functions using local regularization
    • Clément P. Approximation by finite element functions using local regularization RAIRO, Anal. Num. R-2 1975 77-84
    • (1975) RAIRO, Anal. Num. , vol.R-2 , pp. 77-84
    • Clément, P.1
  • 31
    • 0036487117 scopus 로고    scopus 로고
    • Uniqueness of continuous solutions for BV vector fields
    • Colombini F. Lerner N. Uniqueness of continuous solutions for BV vector fields Duke Math. J. 111 2 2002 357-384
    • (2002) Duke Math. J. , vol.111 , Issue.2 , pp. 357-384
    • Colombini, F.1    Lerner, N.2
  • 32
    • 78650731547 scopus 로고    scopus 로고
    • Private email communication
    • Costabel M. Dauge M. Private email communication 2000
    • (2000)
    • Costabel, M.1    Dauge, M.2
  • 33
    • 0003908527 scopus 로고
    • ber die partiellen Differenzengleichungen der mathematischen Physik
    • English translation: On the partial difference equations of mathematical physics IBM J. 1967 215-234
    • Courant R. Friedrichs K. Lewy H. ber die partiellen Differenzengleichungen der mathematischen Physik Mathematische Annalen 100 1 1928 3274 English translation: On the partial difference equations of mathematical physics IBM J. 1967 215-234
    • (1928) Mathematische Annalen , vol.100 , Issue.1 , pp. 3274
    • Courant, R.1    Friedrichs, K.2    Lewy, H.3
  • 34
    • 84966199862 scopus 로고
    • Nonconforming finite elements for the Stokes problem
    • Crouzeix M. Falk R.S. Nonconforming finite elements for the Stokes problem Math. Comp. 52 186 1989 437-456
    • (1989) Math. Comp. , vol.52 , Issue.186 , pp. 437-456
    • Crouzeix, M.1    Falk, R.S.2
  • 35
    • 0015762231 scopus 로고
    • Conforming and non-conforming finite element methods for solving the stationary Stokes problem
    • Crouzeix M. Raviart P.A. Conforming and non-conforming finite element methods for solving the stationary Stokes problem RAIRO Anal. Numér. 8 1973 33-76
    • (1973) RAIRO Anal. Numér. , vol.8 , pp. 33-76
    • Crouzeix, M.1    Raviart, P.A.2
  • 36
    • 0002307515 scopus 로고
    • Stationary Stokes and Navier-Stokes systems on two or three-dimensional domains with corners
    • Dauge M. Stationary Stokes and Navier-Stokes systems on two or three-dimensional domains with corners SIAM J. Math. Anal. 20 1 1989 74-97
    • (1989) SIAM J. Math. Anal. , vol.20 , Issue.1 , pp. 74-97
    • Dauge, M.1
  • 37
    • 0008276077 scopus 로고
    • Neumann and mixed problems on curvilinear polyhedra
    • Dauge M. 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
  • 39
    • 0001424807 scopus 로고    scopus 로고
    • A few remarks on ordinary differential equations
    • Desjardins B. A few remarks on ordinary differential equations Comm. Partial Diff. Equ. 11-12 21 1996 1667-1703
    • (1996) Comm. Partial Diff. Equ. , vol.11-12 , Issue.21 , pp. 1667-1703
    • Desjardins, B.1
  • 40
    • 0002306354 scopus 로고
    • Ordinary differential equations, transport theory and Sobolev spaces
    • Diperna R.J. Lions P.L. Ordinary differential equations, transport theory and Sobolev spaces Invent. Math. 98 1989 511-547
    • (1989) Invent. Math. , vol.98 , pp. 511-547
    • Diperna, R.J.1    Lions, P.L.2
  • 41
    • 0016013907 scopus 로고
    • Thermodynamics, stability, and boundedness of fluids of complexity two and fluids of second grade
    • Dunn J.E. Fosdick R.L. Thermodynamics, stability, and boundedness of fluids of complexity two and fluids of second grade Arch. Ration. Mech. Anal. 56 1974 191-252
    • (1974) Arch. Ration. Mech. Anal. , vol.56 , pp. 191-252
    • Dunn, J.E.1    Fosdick, R.L.2
  • 42
    • 0029289811 scopus 로고
    • Fluids of differential type: Critical review and thermodynamic analysis
    • Dunn J.E. Rajagopal K.R. Fluids of differential type: Critical review and thermodynamic analysis Int. J. Eng. Sci. 33 1995 689-729
    • (1995) Int. J. Eng. Sci. , vol.33 , pp. 689-729
    • Dunn, J.E.1    Rajagopal, K.R.2
  • 43
    • 0035661496 scopus 로고    scopus 로고
    • An explicit right inverse of the divergence operator which is continuous in weighted norms
    • Durán R. Muschietti A. An explicit right inverse of the divergence operator which is continuous in weighted norms Studia Mathematica 148 2001 207-219
    • (2001) Studia Mathematica , vol.148 , pp. 207-219
    • Durán, R.1    Muschietti, A.2
  • 44
    • 84966225382 scopus 로고
    • Sharp maximum norm error estimates for finite element approximations of the Stokes problem in 2 - D
    • Durán R. Nochetto R.H. Wang J. Sharp maximum norm error estimates for finite element approximations of the Stokes problem in 2 - D Math. Comp. 51 184 1988 1177-1192
    • (1988) Math. Comp. , vol.51 , Issue.184 , pp. 1177-1192
    • Durán, R.1    Nochetto, R.H.2    Wang, J.3
  • 46
    • 84865687708 scopus 로고
    • The Dirichlet problem for the Stokes system on Lipschitz domains
    • Fabes E. Kenig C. Verchotta G. The Dirichlet problem for the Stokes system on Lipschitz domains Duke Math. J. 57 3 1988 769-793
    • (1988) Duke Math. J. , vol.57 , Issue.3 , pp. 769-793
    • Fabes, E.1    Kenig, C.2    Verchotta, G.3
  • 47
    • 4243123633 scopus 로고    scopus 로고
    • Mathematical modelling and analysis of viscoelastic fluids of the Oldroyd kind
    • Ciarlet P.G. Lions J.L. VIII 2002 Elsevier North-Holland
    • Fernández Cara E. Guillén González F. Robles Ortega R. Mathematical modelling and analysis of viscoelastic fluids of the Oldroyd kind Handbook of Numerical Analysis Ciarlet P.G. Lions J.L. VIII 2002 Elsevier North-Holland 543-661
    • Handbook of Numerical Analysis , pp. 543-661
    • Fernández Cara, E.1    Guillén González, F.2    Robles Ortega, R.3
  • 48
    • 0020735864 scopus 로고
    • A non-conforming piecewise quadratic finite element on triangles
    • Fortin M. Soulié M. A non-conforming piecewise quadratic finite element on triangles Int. J. Numer. Methods Eng. 19 1983 505-520
    • (1983) Int. J. Numer. Methods Eng. , vol.19 , pp. 505-520
    • Fortin, M.1    Soulié, M.2
  • 49
    • 0018681758 scopus 로고
    • Anomalous features in the model of "Second order fluids"
    • Fosdick R.L. Rajagopal K.R. Anomalous features in the model of "Second order fluids" Arch. Ration. Mech. Anal. 70 1978 145-152
    • (1978) Arch. Ration. Mech. Anal. , vol.70 , pp. 145-152
    • Fosdick, R.L.1    Rajagopal, K.R.2
  • 50
    • 0018061357 scopus 로고
    • Uniqueness and drag for fluids of second grade in steady motion
    • Fosdick R.L. Rajagopal K.R. Uniqueness and drag for fluids of second grade in steady motion Int. J. Non Linear Mech. 13 1978 131-137
    • (1978) Int. J. Non Linear Mech. , vol.13 , pp. 131-137
    • Fosdick, R.L.1    Rajagopal, K.R.2
  • 51
    • 0038506740 scopus 로고    scopus 로고
    • Two-grid finite-element schemes for the steady Navier-Stokes problem in polyhedra
    • Girault V. Lions J.-L. Two-grid finite-element schemes for the steady Navier-Stokes problem in polyhedra Portug. Math. 58 1 2001 25-57
    • (2001) Portug. Math. , vol.58 , Issue.1 , pp. 25-57
    • Girault, V.1    Lions, J.-L.2
  • 52
    • 0035643774 scopus 로고    scopus 로고
    • Two-grid finite-element schemes for the transient Navier-Stokes equations
    • Girault V. Lions J.-L. Two-grid finite-element schemes for the transient Navier-Stokes equations M2AN 35 2001 945-980
    • (2001) M2AN , vol.35 , pp. 945-980
    • Girault, V.1    Lions, J.-L.2
  • 53
    • 16244420155 scopus 로고
    • An analysis of upwind schemes for the Navier-Stokes Equations
    • Girault V. Raviart P.A. An analysis of upwind schemes for the Navier-Stokes Equations SIAM J. Numer. Anal. 19 2 1982 312-333
    • (1982) SIAM J. Numer. Anal. , vol.19 , Issue.2 , pp. 312-333
    • Girault, V.1    Raviart, P.A.2
  • 55
    • 11244280117 scopus 로고    scopus 로고
    • A discontinuous Galerkin method with non-overlapping domain decomposition for the Stokes and Navier-Stokes problems
    • Girault V. Rivière B. Wheeler M.F. A discontinuous Galerkin method with non-overlapping domain decomposition for the Stokes and Navier-Stokes problems Math. Comp. 74 2004 53-84
    • (2004) Math. Comp. , vol.74 , pp. 53-84
    • Girault, V.1    Rivière, B.2    Wheeler, M.F.3
  • 56
    • 34247892445 scopus 로고    scopus 로고
    • On a time-dependent grade-two fluid model in two dimensions
    • Girault V. Saadouni M. On a time-dependent grade-two fluid model in two dimensions Comput. Math. 53 2007 347-360
    • (2007) Comput. Math. , vol.53 , pp. 347-360
    • Girault, V.1    Saadouni, M.2
  • 57
    • 0033544717 scopus 로고    scopus 로고
    • Analysis of a two-dimensional grade-two fluid model with a tangential boundary condition
    • Girault V. Scott L.R. Analysis of a two-dimensional grade-two fluid model with a tangential boundary condition J. Math. Pures Appl. 78 1999 981-1011
    • (1999) J. Math. Pures Appl. , vol.78 , pp. 981-1011
    • Girault, V.1    Scott, L.R.2
  • 58
    • 0035568565 scopus 로고    scopus 로고
    • Finite-element discretizations of a two-dimensional grade-two fluid model
    • Girault V. Scott L.R. Finite-element discretizations of a two-dimensional grade-two fluid model M2AN 35 2002 1007-1053
    • (2002) M2AN , vol.35 , pp. 1007-1053
    • Girault, V.1    Scott, L.R.2
  • 59
    • 0036018012 scopus 로고    scopus 로고
    • Hermite interpolation of non-smooth functions preserving boundary conditions
    • Girault V. Scott L.R. Hermite interpolation of non-smooth functions preserving boundary conditions Math. Comp. 71 2002 1043-1074
    • (2002) Math. Comp. , vol.71 , pp. 1043-1074
    • Girault, V.1    Scott, L.R.2
  • 60
    • 62549117460 scopus 로고    scopus 로고
    • Upwind discretizations of a steady grade-two fluid model in two dimensions
    • Cioranescu D. Lions J.-L. (College de France Seminar, Volume XIV)
    • Girault V. Scott L.R. Upwind discretizations of a steady grade-two fluid model in two dimensions Nonlinear Partial Differential Equations and their Applications 31 2002 393-414 Cioranescu D. Lions J.-L. (College de France Seminar, Volume XIV)
    • (2002) Nonlinear Partial Differential Equations and their Applications , vol.31 , pp. 393-414
    • Girault, V.1    Scott, L.R.2
  • 61
    • 0037595549 scopus 로고    scopus 로고
    • A quasi-local interpolation operator preserving the discrete divergence
    • Girault V. Scott L.R. A quasi-local interpolation operator preserving the discrete divergence Calcolo 40 2003 1-19
    • (2003) Calcolo , vol.40 , pp. 1-19
    • Girault, V.1    Scott, L.R.2
  • 62
    • 77956077099 scopus 로고    scopus 로고
    • On a time-dependent transport equation in a Lipschitz domain
    • Girault V. Scott L.R. On a time-dependent transport equation in a Lipschitz domain SIAM J. Math. Anal. 42 2010 1721-1731
    • (2010) SIAM J. Math. Anal. , vol.42 , pp. 1721-1731
    • Girault, V.1    Scott, L.R.2
  • 63
    • 77955772358 scopus 로고    scopus 로고
    • L p and W 1, p regularity of the solution of a steady transportequation
    • Girault V. Tartar L. L p and W 1, p regularity of the solution of a steady transportequation C. R. Acad. Sci. Paris, Sir I 348 2010 885-890
    • (2010) C. R. Acad. Sci. Paris, Sir I , vol.348 , pp. 885-890
    • Girault, V.1    Tartar, L.2
  • 64
    • 67649646329 scopus 로고    scopus 로고
    • Finite element methods for incompressible viscous flow
    • Ciarlet P.G. Lions J.L. Elsevier North-Holland
    • Glowinski R. Finite element methods for incompressible viscous flow Handbook of Numerical Analysis 9 2003 Ciarlet P.G. Lions J.L. Elsevier North-Holland 9-1176
    • (2003) Handbook of Numerical Analysis , vol.9 , pp. 9-1176
    • Glowinski, R.1
  • 65
    • 0004088932 scopus 로고    scopus 로고
    • Pitman Monographs and Studies in Mathematics Volume 24 1985 Pitman Boston, MA
    • Grisvard P. Elliptic Problems in Nonsmooth Domains Pitman Monographs and Studies in Mathematics Volume 24 1985 Pitman Boston, MA
    • Elliptic Problems in Nonsmooth Domains
    • Grisvard, P.1
  • 66
    • 78650740654 scopus 로고    scopus 로고
    • Freefem++, Second Edition, Version 2.24-2-2 Laboratoire J.-L. Lions UPMC, Paris
    • Hecht F. Le Hyaric A. Pironneau O. Ohtsuka K. Freefem++, Second Edition, Version 2.24-2-2 Laboratoire J.-L. Lions UPMC, Paris 2008
    • (2008)
    • Hecht, F.1    Le Hyaric, A.2    Pironneau, O.3    Ohtsuka, K.4
  • 67
    • 11744318899 scopus 로고    scopus 로고
    • Euler-Poincaré models of ideal fluids with nonlinear dispersion
    • Holm D.D. Marsden J.E. Ratiu T.S. Euler-Poincaré models of ideal fluids with nonlinear dispersion Phys. Rev. Lett. 349 1998 4173-4177
    • (1998) Phys. Rev. Lett. , vol.349 , pp. 4173-4177
    • Holm, D.D.1    Marsden, J.E.2    Ratiu, T.S.3
  • 68
    • 0001971504 scopus 로고    scopus 로고
    • The Euler-Poincaré equations and semidirect products with applications to continuum theories
    • Holm D.D. Marsden J.E. Ratiu T.S. The Euler-Poincaré equations and semidirect products with applications to continuum theories Adv. Math. 137 1998 1-81
    • (1998) Adv. Math. , vol.137 , pp. 1-81
    • Holm, D.D.1    Marsden, J.E.2    Ratiu, T.S.3
  • 69
    • 0015566427 scopus 로고
    • A numerical solution of the Navier-Stokes equations using the finite element technique
    • Hood P. Taylor C. A numerical solution of the Navier-Stokes equations using the finite element technique Comp. Fluids 1 1973 73-100
    • (1973) Comp. Fluids , vol.1 , pp. 73-100
    • Hood, P.1    Taylor, C.2
  • 70
    • 84944818416 scopus 로고
    • Uber die Aufangswertaufgabe fur die hydrodynamischen Grundleichungen
    • Hopf E. Uber die Aufangswertaufgabe fur die hydrodynamischen Grundleichungen Math. Nachr. 4 1951 213-231
    • (1951) Math. Nachr. , vol.4 , pp. 213-231
    • Hopf, E.1
  • 72
    • 0018056277 scopus 로고
    • A simple finite element scheme for developping upwind finite elements
    • Hugues T.J.R. A simple finite element scheme for developping upwind finite elements Int. J. Numer. Methods Eng. 12 1978 1359-1365
    • (1978) Int. J. Numer. Methods Eng. , vol.12 , pp. 1359-1365
    • Hugues, T.J.R.1
  • 76
    • 0001415204 scopus 로고
    • A regularity for the Stokes problem in a convex polygon
    • Kellog R.B. Osborn J.E. A regularity for the Stokes problem in a convex polygon J. Funct. Anal. 21 1976 397-431
    • (1976) J. Funct. Anal. , vol.21 , pp. 397-431
    • Kellog, R.B.1    Osborn, J.E.2
  • 78
    • 0001740980 scopus 로고    scopus 로고
    • Contributions to the Theory of Partial Differential Equations 1954 Princeton
    • Lax P. Milgram N. Parabolic Equations Contributions to the Theory of Partial Differential Equations 1954 Princeton
    • Parabolic Equations
    • Lax, P.1    Milgram, N.2
  • 79
    • 0003068173 scopus 로고
    • Etude de diverses équations intégrales nonlinéaires et de quelques problèmes que pose l'hydrodynamique
    • Leray J. Etude de diverses équations intégrales nonlinéaires et de quelques problèmes que pose l'hydrodynamique J. Math. Pures Appl. 12 1933 1-82
    • (1933) J. Math. Pures Appl. , vol.12 , pp. 1-82
    • Leray, J.1
  • 84
    • 84951671794 scopus 로고
    • Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind
    • Nitsche J. Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind Abh. Math. Hamburg. 36 1970 9-15
    • (1970) Abh. Math. Hamburg , vol.36 , pp. 9-15
    • Nitsche, J.1
  • 85
    • 0003931752 scopus 로고
    • Thèse de 3ème Cycle de l'Université Pierre et Marie Curie, Paris VI
    • Ouazar, E.H. (1981). Sur les Fluides de Second Grade, Thèse de 3ème Cycle de l'Université Pierre et Marie Curie, Paris VI.
    • (1981) Sur les Fluides de Second Grade
    • Ouazar, E.H.1
  • 87
    • 0001469934 scopus 로고
    • Espaces d'interpolation et théorème de Soboleff
    • Peetre J. Espaces d'interpolation et théorème de Soboleff Ann. Inst. Fourier 16 1966 279-317
    • (1966) Ann. Inst. Fourier , vol.16 , pp. 279-317
    • Peetre, J.1
  • 89
    • 78650720444 scopus 로고
    • Théorème de densité résultant du lemme de Friedrichs, Report, Diplôme d'Etudes Approfondies, Advisor C. Goulaouic, Université de Rennes
    • Puel, J.P., Roptin, M.C. (1967). Lemme de Friedrichs. Théorème de densité résultant du lemme de Friedrichs, Report, Diplôme d'Etudes Approfondies, Advisor C. Goulaouic, Université de Rennes.
    • (1967) Lemme de Friedrichs
    • Puel, J.P.1    Roptin, M.C.2
  • 90
    • 0000762280 scopus 로고
    • On boundary conditions for fluids of the differential type
    • Sequeira A., Plenum Press
    • Rajagopal K.R. On boundary conditions for fluids of the differential type Navier-Stokes Equations and Related Problems 1995 Sequeira A., Plenum Press
    • (1995) Navier-Stokes Equations and Related Problems
    • Rajagopal, K.R.1
  • 91
    • 0002230177 scopus 로고
    • Some remarks on boundary conditions for the flow of fluids of the differential type
    • Hemisphere Press
    • Rajagopal K.R. Kaloni P.N. Some remarks on boundary conditions for the flow of fluids of the differential type Continuum Mechanics and its Applications 1989 Hemisphere Press
    • (1989) Continuum Mechanics and its Applications
    • Rajagopal, K.R.1    Kaloni, P.N.2
  • 93
    • 0001526376 scopus 로고
    • Stress-deformation relations for isotropic materials
    • Rivlin R.S. Ericksen J.L. Stress-deformation relations for isotropic materials Arch. Ration. Mech. Anal. 4 1955 323-425
    • (1955) Arch. Ration. Mech. Anal. , vol.4 , pp. 323-425
    • Rivlin, R.S.1    Ericksen, J.L.2
  • 97
    • 84966200902 scopus 로고
    • Finite element interpolation of non-smooth functions satisfying boundary conditions
    • Scott L.R. Zhang S. Finite element interpolation of non-smooth functions satisfying boundary conditions Math. Comp. 54 1990 483-493
    • (1990) Math. Comp. , vol.54 , pp. 483-493
    • Scott, L.R.1    Zhang, S.2
  • 99
    • 34247889595 scopus 로고
    • Compact sets in the space L p (0, T;B)
    • Simon J. Compact sets in the space L p (0, T;B) Ann. Math. Pures Appl. 146 1990 1093-1117
    • (1990) Ann. Math. Pures Appl. , vol.146 , pp. 1093-1117
    • Simon, J.1
  • 101
    • 84968512389 scopus 로고
    • Analysis of finite element methods for the Stokes problem: a unified approach
    • Stenberg R. Analysis of finite element methods for the Stokes problem: a unified approach Math. Comp. 42 1984 9-23
    • (1984) Math. Comp. , vol.42 , pp. 9-23
    • Stenberg, R.1
  • 102
    • 0003942816 scopus 로고
    • Publications Mathématiques d'Orsay, Université Paris-Sud, Orsay
    • Tartar L. Topics in Nonlinear Analysis 1978 Publications Mathématiques d'Orsay, Université Paris-Sud, Orsay
    • (1978) Topics in Nonlinear Analysis
    • Tartar, L.1
  • 106
    • 78650757098 scopus 로고    scopus 로고
    • An Introduction to the Mechanics of Fluids, Modeling and Simulation
    • Birkhauser Basel
    • Truesdell C. Rajagopal K.R. An Introduction to the Mechanics of Fluids, Modeling and Simulation Science, Engineering and Technology 2000 Birkhauser Basel
    • (2000) Science, Engineering and Technology
    • Truesdell, C.1    Rajagopal, K.R.2
  • 107
    • 0002682177 scopus 로고
    • Error estimates for a mixed finite element approximation of the Stokes equations
    • Verfürth R. Error estimates for a mixed finite element approximation of the Stokes equations RAIRO Anal. Numér. 18 2 1984 175-182
    • (1984) RAIRO Anal. Numér. , vol.18 , Issue.2 , pp. 175-182
    • Verfürth, R.1
  • 109
    • 27744571569 scopus 로고    scopus 로고
    • Convergence of the discontinuous Galerkin method for discontinuous solutions
    • Walkington N.J. Convergence of the discontinuous Galerkin method for discontinuous solutions SIAM J. Numer. Anal. 42 2005 1801-1817
    • (2005) SIAM J. Numer. Anal. , vol.42 , pp. 1801-1817
    • Walkington, N.J.1


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