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Volumn 48, Issue 12, 2005, Pages 1375-1414

Regularized finite element discretizations of a grade-two fluid model

Author keywords

Finite elements; Non Newtonian fluids; Regularization method

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; FINITE ELEMENT METHOD; GALERKIN METHODS; MATHEMATICAL MODELS; NUMERICAL METHODS;

EID: 23844454098     PISSN: 02712091     EISSN: None     Source Type: Journal    
DOI: 10.1002/fld.949     Document Type: Article
Times cited : (3)

References (38)
  • 2
    • 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. Mathematical Methods in the Applied Sciences 1999; 22:655-687.
    • (1999) Mathematical Methods in the Applied Sciences , vol.22 , pp. 655-687
    • Bernard, J.-M.1
  • 6
    • 0016013907 scopus 로고
    • Thermodynamics, stability, and boundedness of fluids of complexity two and fluids of second grade
    • Dunn JE, Fosdick RL. Thermodynamics, stability, and boundedness of fluids of complexity two and fluids of second grade. Archives for Rational Mechanics anti Analysis 1974; 56:191-252.
    • (1974) Archives for Rational Mechanics Anti Analysis , vol.56 , pp. 191-252
    • Dunn, J.E.1    Fosdick, R.L.2
  • 8
    • 0003710974 scopus 로고    scopus 로고
    • Fluides de second et troisième grade en dimension trois: Solution globale et régularité
    • Thèse de l'Université Pierre et Marie Curie, Paris
    • Bernard J-M. Fluides de second et troisième grade en dimension trois: solution globale et régularité. Thèse de l'Université Pierre et Marie Curie, Paris, 1998.
    • (1998)
    • Bernard, J.-M.1
  • 9
    • 0003931752 scopus 로고
    • Sur les fluides de second grade
    • Thèse de l'Université Pierre et Marie Curie, Paris
    • Ouazar EH. Sur les fluides de second grade. Thèse de l'Université Pierre et Marie Curie, Paris, 1981.
    • (1981)
    • Ouazar, E.H.1
  • 10
    • 33645247288 scopus 로고    scopus 로고
    • Least-squares methods for the simulation of the flow of an incompressible fluid of second grade
    • Ph.D. Thesis, The University of Houston
    • Park KH. Least-squares methods for the simulation of the flow of an incompressible fluid of second grade. Ph.D. Thesis, The University of Houston, 1998.
    • (1998)
    • Park, K.H.1
  • 11
    • 0002167114 scopus 로고
    • Nonsteady channel flow of ice as a modified second-order fluid with power-law viscosity
    • Man C-S. Nonsteady channel flow of ice as a modified second-order fluid with power-law viscosity. Archives for Rational Mechanics and Analysis 1992; 119:35-57.
    • (1992) Archives for Rational Mechanics and Analysis , vol.119 , pp. 35-57
    • Man, C.-S.1
  • 12
    • 11744318899 scopus 로고    scopus 로고
    • Euler-Poincaré models of ideal fluids with nonlinear dispersion
    • Holm DD, Marsden JE, Ratiu TS. Euler-Poincaré models of ideal fluids with nonlinear dispersion. Physics Review Letters 1998; 349: 4173-4177.
    • (1998) Physics Review Letters , vol.349 , pp. 4173-4177
    • Holm, D.D.1    Marsden, J.E.2    Ratiu, T.S.3
  • 13
    • 0033544717 scopus 로고    scopus 로고
    • Analysis of a two-dimensional grade-two fluid model with a tangential boundary condition
    • Girault V, Scott LR. Analysis of a two-dimensional grade-two fluid model with a tangential boundary condition. Journal de Mathématiques Pares et Appliquées 1999; 78:981-1011.
    • (1999) Journal De Mathématiques Pares Et Appliquées , vol.78 , pp. 981-1011
    • Girault, V.1    Scott, L.R.2
  • 14
    • 0035568565 scopus 로고    scopus 로고
    • Finite-element discretizations of a two-dimensional grade-two fluid model
    • Girault V, Scott LR. Finite-element discretizations of a two-dimensional grade-two fluid model. Modél. Math. et Anal. Numér. 2001; 35:1007-1053.
    • (2001) Modél. Math. Et Anal. Numér. , vol.35 , pp. 1007-1053
    • Girault, V.1    Scott, L.R.2
  • 15
    • 0009261778 scopus 로고
    • Boundary-value problems for a class of first order partial differential equations in Sobolev spaces and applications to the Euler flow
    • Beirão da Veiga H. Boundary-value problems for a class of first order partial differential equations in Sobolev spaces and applications to the Euler flow. Rendiconti del Seminario Matematico Universita di Padova 1988; 79:247-273.
    • (1988) Rendiconti Del Seminario Matematico Universita Di Padova , vol.79 , pp. 247-273
    • Beirão da Veiga, H.1
  • 17
  • 18
    • 33645266349 scopus 로고    scopus 로고
    • Robust a posteriori error estimates for stationary convection-diffusion equations
    • submitted
    • Verfürth R. Robust a posteriori error estimates for stationary convection-diffusion equations, submitted.
    • Verfürth, R.1
  • 21
    • 23844543126 scopus 로고
    • Sur les problèmes aux limites du type dérivée oblique
    • Lions J-L. Sur les problèmes aux limites du type dérivée oblique. Annals of Mathematics 1956; 64:207-239.
    • (1956) Annals of Mathematics , vol.64 , pp. 207-239
    • Lions, J.-L.1
  • 23
    • 0002306354 scopus 로고
    • Ordinary differential equations, transport theory and Sobolev spaces
    • DiPerna RJ, Lions P-L. Ordinary differential equations, transport theory and Sobolev spaces. Inventiones Mathematicae 1989; 98: 511-547.
    • (1989) Inventiones Mathematicae , vol.98 , pp. 511-547
    • DiPerna, R.J.1    Lions, P.-L.2
  • 24
    • 0039207306 scopus 로고
    • Contribución al estudio teórico de algunas E.D.P. no lineales relacionadas con fluidos no Newtonianos
    • Thesis, Universidad de Sevilla
    • Ortega RR. Contribución al estudio teórico de algunas E.D.P. no lineales relacionadas con fluidos no Newtonianos. Thesis, Universidad de Sevilla, 1995.
    • (1995)
    • Ortega, R.R.1
  • 26
    • 0008276077 scopus 로고
    • Neumann and mixed problems on curvilinear polyhedra
    • Dauge M. Neumann and mixed problems on curvilinear polyhedra. Integr. Equat. Oper. Th. 1992; 15:227-264.
    • (1992) Integr. Equat. Oper. Th. , vol.15 , pp. 227-264
    • Dauge, M.1
  • 27
    • 34250392866 scopus 로고
    • Best constant in Sobolev inequality
    • serie IV
    • Talenti G. Best constant in Sobolev inequality. Ann. Math. Pura Appl., serie IV 1976; 110:353-372.
    • (1976) Ann. Math. Pura Appl. , vol.110 , pp. 353-372
    • Talenti, G.1
  • 28
    • 84918708465 scopus 로고
    • Consistency, stability, a priori and a posteriori errors for Petrov-Galerkin methods applied to nonlinear problems
    • Pousin J, Rappaz J. Consistency, stability, a priori and a posteriori errors for Petrov-Galerkin methods applied to nonlinear problems. Numerische Mathematik 1994; 69:213-231.
    • (1994) Numerische Mathematik , vol.69 , pp. 213-231
    • Pousin, J.1    Rappaz, J.2
  • 29
    • 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. Mathematics of Computation 1985; 44:71-79.
    • (1985) Mathematics of Computation , vol.44 , pp. 71-79
    • Bernardi, C.1    Raugel, G.2
  • 30
    • 0002435262 scopus 로고
    • Finite dimensional approximation of nonlinear problems. Part I: Branches of nonsingular solutions
    • Brezzi F, Rappaz J, Raviart P-A. Finite dimensional approximation of nonlinear problems. Part I: Branches of nonsingular solutions. Numerische Mathematik 1980; 36:1-25.
    • (1980) Numerische Mathematik , vol.36 , pp. 1-25
    • Brezzi, F.1    Rappaz, J.2    Raviart, P.-A.3
  • 32
    • 0003896053 scopus 로고
    • Problèmes aux limites non homogènes et applications
    • Dunod: Paris
    • Lions J-L, Magenes E. Problèmes aux limites non homogènes et applications, vol. 1. Dunod: Paris, 1968.
    • (1968) , vol.1
    • Lions, J.-L.1    Magenes, E.2
  • 34
    • 0001175293 scopus 로고
    • A mixed finite element method for second order elliptic problems
    • Lecture Notes in Mathematics, Springer: Berlin
    • Raviart P-A, Thomas J-M. A mixed finite element method for second order elliptic problems. In Mathematical Aspects of Finite Element Methods, Lecture Notes in Mathematics, vol. 606. Springer: Berlin, 1977; 292-315.
    • (1977) Mathematical Aspects of Finite Element Methods , vol.606 , pp. 292-315
    • Raviart, P.-A.1    Thomas, J.-M.2
  • 35
    • 33645258867 scopus 로고    scopus 로고
    • FreeFem++, see www.freefem.org
    • Hecht F, Pironneau O. FreeFem++, see www.freefem.org.
    • Hecht, F.1    Pironneau, O.2
  • 37
    • 2942687919 scopus 로고    scopus 로고
    • Lax theorem and finite volume schemes
    • Després B. Lax theorem and finite volume schemes. Mathematics of Computation 2004; 73:1203-1234.
    • (2004) Mathematics of Computation , vol.73 , pp. 1203-1234
    • Després, B.1
  • 38
    • 0003595398 scopus 로고    scopus 로고
    • Maillages, applications aux éléments finis
    • Hermès: Paris
    • Frey PJ, George P-L. Maillages, applications aux éléments finis. Hermès: Paris, 1999.
    • (1999)
    • Frey, P.J.1    George, P.-L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.