메뉴 건너뛰기




Volumn 96, Issue 1, 2003, Pages 153-184

Error estimates for the numerical approximation of time-dependent flow of Bingham fluid in cylindrical pipes by the regularization method

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0742271736     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00211-003-0469-6     Document Type: Article
Times cited : (9)

References (68)
  • 1
    • 0002552584 scopus 로고
    • Discretization of evolution inequalities
    • F. Colombini-A. Marino-L. Modica-S. Spagnolo editors, Birkäuser, Boston
    • Baiocchi, C.: Discretization of evolution inequalities. In: Partial Differential Equations and the Calculus of Variations, F. Colombini-A. Marino-L. Modica-S. Spagnolo editors, Birkäuser, Boston, 1989, pp. 59-92
    • (1989) Partial Differential Equations and the Calculus of Variations , pp. 59-92
    • Baiocchi, C.1
  • 3
    • 84966231549 scopus 로고
    • An error estimate for the truncation method for the solution of parabolic obstacle variational inequalities
    • Berger, A.E., Falk, R.S.: An error estimate for the truncation method for the solution of parabolic obstacle variational inequalities. Math. Comput. 31, 619-628 (1977)
    • (1977) Math. Comput. , vol.31 , pp. 619-628
    • Berger, A.E.1    Falk, R.S.2
  • 4
    • 0002239265 scopus 로고
    • Monotonicity methods in Hilbert spaces and some applications to nonlinear partial differential equations
    • E. Zarantonello, Ed., Acad. Press
    • Brézis, H.: Monotonicity methods in Hilbert spaces and some applications to nonlinear partial differential equations. In: Contributions to Nonlinear Functional Analysis. E. Zarantonello, Ed., Acad. Press, 1971, pp. 101-156
    • (1971) Contributions to Nonlinear Functional Analysis , pp. 101-156
    • Brézis, H.1
  • 5
    • 0001968839 scopus 로고
    • Problèmes Unilatéraux
    • Brézis, H.: Problèmes Unilatéraux. J. Math, pures et appl. 51, 1-168 (1972)
    • (1972) J. Math, Pures et Appl. , vol.51 , pp. 1-168
    • Brézis, H.1
  • 6
    • 0001585127 scopus 로고
    • Sur la regularite de la solution d'inequations elliptiques
    • Brézis, H., Stampacchia, G.: Sur la regularite de la solution d'inequations elliptiques. Bull. Soc. Math. France 96, 254-265 (1968)
    • (1968) Bull. Soc. Math. France , vol.96 , pp. 254-265
    • Brézis, H.1    Stampacchia, G.2
  • 7
    • 0000947683 scopus 로고
    • Error estimates for the finite element solution of variational inequalities
    • Brezzi, F., Hager, W.W., Raviart, P.A.: Error estimates for the finite element solution of variational inequalities. Numer. Math. 28, 431-443 (1977)
    • (1977) Numer. Math. , vol.28 , pp. 431-443
    • Brezzi, F.1    Hager, W.W.2    Raviart, P.A.3
  • 8
    • 0016093926 scopus 로고
    • On the existence, uniqueness, and approximation of saddle-point problems arising from Lagrange multiplier
    • Brezzi, F.: On the existence, uniqueness, and approximation of saddle-point problems arising from Lagrange multiplier. RAIRO Anal. Numér. 8(R-2), 129-151 (1975)
    • (1975) RAIRO Anal. Numér. , vol.8 , Issue.R-2 , pp. 129-151
    • Brezzi, F.1
  • 9
    • 21744461963 scopus 로고    scopus 로고
    • Regularization procedures of singular free boundary problems in rotational Bingham flows
    • Comparini, E.: Regularization procedures of singular free boundary problems in rotational Bingham flows. Z. Angew. Math. Mech. 77, 543-554 (1997)
    • (1997) Z. Angew. Math. Mech. , vol.77 , pp. 543-554
    • Comparini, E.1
  • 10
    • 0003083769 scopus 로고    scopus 로고
    • Fluid of a Bingham fluid in contact with Newtonian fluid
    • Comparini, E., Mannucci, P.: Fluid of a Bingham fluid in contact with Newtonian fluid. J. Math. Anal. Appl. 227, 359-381 (1998)
    • (1998) J. Math. Anal. Appl. , vol.227 , pp. 359-381
    • Comparini, E.1    Mannucci, P.2
  • 11
    • 0013116220 scopus 로고
    • Model for the flow of a yield fluid through a porous-medium
    • Chaplain, V., Mills, P., Guiffant, G., Cerasi, P.: Model for the flow of a yield fluid through a porous-medium. Journal de Physique 2 2, 2145-2158 (1992)
    • (1992) Journal de Physique 2 , vol.2 , pp. 2145-2158
    • Chaplain, V.1    Mills, P.2    Guiffant, G.3    Cerasi, P.4
  • 12
    • 0042235076 scopus 로고
    • A penalty method approach to strong solutions of some nonlinear parabolic unilateral problems
    • Donati, F.: A penalty method approach to strong solutions of some nonlinear parabolic unilateral problems. Numerical Analysis, Theory, Methods & Applications 6(6), 585-597 (1982)
    • (1982) Numerical Analysis, Theory, Methods & Applications , vol.6 , Issue.6 , pp. 585-597
    • Donati, F.1
  • 14
  • 15
    • 0032029645 scopus 로고    scopus 로고
    • Drag and fall velocity of a spherical particle in generalized Newtonian and viscoplastic fluids
    • Dolejs, V., Dolecek, P., Siska, B.: Drag and fall velocity of a spherical particle in generalized Newtonian and viscoplastic fluids. Chem. Eng. Process 37, 189-195 (1998)
    • (1998) Chem. Eng. Process , vol.37 , pp. 189-195
    • Dolejs, V.1    Dolecek, P.2    Siska, B.3
  • 17
    • 0026994309 scopus 로고
    • Behavior of A Bingham-like viscous-fluid in lubrication flows
    • Dorier, C., Tichy, J.: Behavior of A Bingham-like viscous-fluid in lubrication flows. J. Non-Newtonian Fluid Mech. 45, 291-310 (1992)
    • (1992) J. Non-Newtonian Fluid Mech. , vol.45 , pp. 291-310
    • Dorier, C.1    Tichy, J.2
  • 18
    • 0000003984 scopus 로고
    • Error estimates for the approximation of a class of variational inequalities
    • Falk, R.S.: Error estimates for the approximation of a class of variational inequalities. Math. Comp. 28, 963-971 (1974)
    • (1974) Math. Comp. , vol.28 , pp. 963-971
    • Falk, R.S.1
  • 19
    • 0345904395 scopus 로고
    • ∞-Error estimate for an approximation of a parabolic variational inequality
    • ∞-Error estimate for an approximation of a parabolic variational inequality. Numer. Math. 50, 557-565 (1987)
    • (1987) Numer. Math. , vol.50 , pp. 557-565
    • Fetter, A.1
  • 22
    • 0026173603 scopus 로고
    • On the imposition of friction boundary-conditions for the numerical-simulation of Bingham fluid-flows
    • Fortin, A., Cote, D., Tanguy, P.A.: On the imposition of friction boundary-conditions for the numerical-simulation of Bingham fluid-flows. Comput. Method Appl. Mech. Eng. 88, 97-109 (1991)
    • (1991) Comput. Method Appl. Mech. Eng. , vol.88 , pp. 97-109
    • Fortin, A.1    Cote, D.2    Tanguy, P.A.3
  • 23
    • 0016557040 scopus 로고
    • Kinderlehrer, D.: A one phase Stefan problem
    • Friedman, A., Kinderlehrer, D.: A one phase Stefan problem. Indiana Univ. Math. J. 24, 1005-1035 (1975)
    • (1975) Indiana Univ. Math. J. , vol.24 , pp. 1005-1035
    • Friedman, A.1
  • 24
    • 0032122352 scopus 로고    scopus 로고
    • Stratified exchange flows of two Bingham fluids in an inclined slot
    • Frigaard, I.A.: Stratified exchange flows of two Bingham fluids in an inclined slot. J. Non-Newtonian Fluid Mech. 78, 61-87 (1998)
    • (1998) J. Non-Newtonian Fluid Mech. , vol.78 , pp. 61-87
    • Frigaard, I.A.1
  • 25
    • 0031104822 scopus 로고    scopus 로고
    • Flow characteristics of waxy crude oils in laboratory experimental loops
    • Farina, A., Fasano, A.: Flow characteristics of waxy crude oils in laboratory experimental loops. Math. Comput. Modeling 25, 75-86 (1997)
    • (1997) Math. Comput. Modeling , vol.25 , pp. 75-86
    • Farina, A.1    Fasano, A.2
  • 26
    • 0032324706 scopus 로고    scopus 로고
    • Uniaxial exchange flows of two Bingham fluids in a cylindrical duct
    • Frigaard, I.A., Scherzer, O.: Uniaxial exchange flows of two Bingham fluids in a cylindrical duct. IMA J. Appl. Math. 61, 237-266 (1998)
    • (1998) IMA J. Appl. Math. , vol.61 , pp. 237-266
    • Frigaard, I.A.1    Scherzer, O.2
  • 27
    • 0002608770 scopus 로고
    • Application of the method of multipliers to variational inequalities
    • M. Fortin and R. Glowinski. eds., North-Holland
    • Gabay, D.: Application of the method of multipliers to variational inequalities, In: Augmented Lagrangian Methods. M. Fortin and R. Glowinski. eds., North-Holland, 1983
    • (1983) Augmented Lagrangian Methods
    • Gabay, D.1
  • 28
    • 0039607401 scopus 로고
    • An error estimate for an approximation of a parabolic variational inequality
    • Gastaldi, L., Gilardi, G.: An error estimate for an approximation of a parabolic variational inequality. Bollettino U. M. I. (6) 1-b 1982, pp. 501-521
    • (1982) Bollettino U. M. I. (6) , vol.1 B , pp. 501-521
    • Gastaldi, L.1    Gilardi, G.2
  • 30
    • 0016347794 scopus 로고
    • Sur l'écoulement d'un fluide de Bingham dans une conduite cylindrique
    • Glowinski, R.: Sur l'écoulement d'un fluide de Bingham dans une conduite cylindrique. Journal de Mécanique 13, 601-621 (1974)
    • (1974) Journal de Mécanique , vol.13 , pp. 601-621
    • Glowinski, R.1
  • 31
    • 0040740124 scopus 로고
    • Splitting methods for the numerical solution of the incompressible Navier-Stokes equations
    • Optimization Software, New York
    • Glowinski, R.: Splitting methods for the numerical solution of the incompressible Navier-Stokes equations. In: Vistas in applied Mathematics, Optimization Software, New York 1986, pp. 57-95
    • (1986) Vistas in Applied Mathematics , pp. 57-95
    • Glowinski, R.1
  • 34
    • 0742267304 scopus 로고
    • Sur l'approximation par éléments finis d'ordre un et la résolution par pénalisation-dualité d'une classe de problèmes de Dirichlet non linéaires
    • Glowinski, R., Marrocco, A.: Sur l'approximation par éléments finis d'ordre un et la résolution par pénalisation-dualité d'une classe de problèmes de Dirichlet non linéaires. C.R. Acad. Sci. Paris 278A, 1649-1652 (1974)
    • (1974) C.R. Acad. Sci. Paris , vol.278 A , pp. 1649-1652
    • Glowinski, R.1    Marrocco, A.2
  • 35
    • 84915673057 scopus 로고
    • On the solution of a class of nonlinear Dirichlet problems by a penalty-duality method and finite elements of order one
    • Optimization Techniques: IFIP Technical Conference, NOVOSSIBIRSK, U.S.S.R., June, ed. by G.I. Marchuk, Springer, Berlin, Heidelberg, New York
    • Glowinski, R., Marrocco, A.: On the solution of a class of nonlinear Dirichlet problems by a penalty-duality method and finite elements of order one. In: Optimization Techniques: IFIP Technical Conference, NOVOSSIBIRSK, U.S.S.R., June 1974, ed. by G.I. Marchuk, Lecture Notes in Computer Sciences, Vol. 27 Springer, Berlin, Heidelberg, New York 1975, pp. 327-333
    • (1974) Lecture Notes in Computer Sciences , vol.27 , pp. 327-333
    • Glowinski, R.1    Marrocco, A.2
  • 36
    • 0017532939 scopus 로고
    • Numerical solution of two-dimensional magneto-static problems by augmented Lagrangian methods
    • Glowinski, R., Marrocco, A.: Numerical solution of two-dimensional magneto-static problems by augmented Lagrangian methods. Comput. Mech. Appl. Mech. Eng. 12, 33-46 (1977)
    • (1977) Comput. Mech. Appl. Mech. Eng. , vol.12 , pp. 33-46
    • Glowinski, R.1    Marrocco, A.2
  • 37
    • 0020669030 scopus 로고
    • Calcul à la rupture: Régularisation de Norton-Hoff et Lagrangien augmenté
    • Guennouni, T., Le Tallec, P.: Calcul à la rupture: Régularisation de Norton-Hoff et Lagrangien augmenté. J. Mécanique 2, 75-99 (1982)
    • (1982) J. Mécanique , vol.2 , pp. 75-99
    • Guennouni, T.1    Le Tallec, P.2
  • 38
    • 0023310834 scopus 로고
    • Error Estimates for the finite Element Solution of Quasilinear Obstacle Problems
    • Hafner, K.: Error Estimates for the finite Element Solution of Quasilinear Obstacle Problems. Numer. Funct. Anal. and Optimiz. 9, 415-433 (1987)
    • (1987) Numer. Funct. Anal. and Optimiz. , vol.9 , pp. 415-433
    • Hafner, K.1
  • 39
    • 38249015052 scopus 로고
    • Quantitative error estimate in modeling the laminar stationary flow of a Bingham fluid
    • Han, W.M.: Quantitative error estimate in modeling the laminar stationary flow of a Bingham fluid. Appl. Math. Comput. 47, 15-24 (1992)
    • (1992) Appl. Math. Comput. , vol.47 , pp. 15-24
    • Han, W.M.1
  • 40
    • 0034372845 scopus 로고    scopus 로고
    • Steady Bingham fluid flow in cylindrical pipes: A time dependent approach to the iterative solution
    • He, J.W., Glowinski, R.: Steady Bingham fluid flow in cylindrical pipes: a time dependent approach to the iterative solution. Num. Linear Algebra with Appl. 7, 381-482 (2000)
    • (2000) Num. Linear Algebra with Appl. , vol.7 , pp. 381-482
    • He, J.W.1    Glowinski, R.2
  • 41
    • 0029328892 scopus 로고
    • On the determination of plug-flow region in Bingham fluids through the application of variational inequalities
    • Huilgol, R.R., Panizza, M.P.: On the determination of plug-flow region in Bingham fluids through the application of variational inequalities. J. Non-Newtonian Fluid Mech. 58, 207-217 (1995)
    • (1995) J. Non-Newtonian Fluid Mech. , vol.58 , pp. 207-217
    • Huilgol, R.R.1    Panizza, M.P.2
  • 42
    • 0033514332 scopus 로고    scopus 로고
    • Modeling of non-hydroplaning mudflows on continental slopes
    • Huang, X., Garcia, M.H.: Modeling of non-hydroplaning mudflows on continental slopes. Marine Geology 154, 131-142 (1999)
    • (1999) Marine Geology , vol.154 , pp. 131-142
    • Huang, X.1    Garcia, M.H.2
  • 43
    • 0032204470 scopus 로고    scopus 로고
    • A Herschel-Bulkley model for mud flow down a slope
    • Huang, X., Garcia, M.H.: A Herschel-Bulkley model for mud flow down a slope. J. Fluid Mech. 374, 305-333 (1998)
    • (1998) J. Fluid Mech. , vol.374 , pp. 305-333
    • Huang, X.1    Garcia, M.H.2
  • 44
    • 0742301914 scopus 로고
    • Convergent approximations in parabolic variational inequalities II: Hamilton-Jacobi inequalities
    • Jerome, J.: Convergent approximations in parabolic variational inequalities II: Hamilton-Jacobi inequalities. Appl. Math. Optim. 8, 265-274 (1982)
    • (1982) Appl. Math. Optim. , vol.8 , pp. 265-274
    • Jerome, J.1
  • 45
    • 0016993703 scopus 로고
    • A convergence estimate for an approximation of a parabolic variational inequality
    • Johnson, C.: A convergence estimate for an approximation of a parabolic variational inequality. SIAM J. Numer. Anal. 13, 599-606 (1976)
    • (1976) SIAM J. Numer. Anal. , vol.13 , pp. 599-606
    • Johnson, C.1
  • 46
    • 0742319513 scopus 로고
    • Semidiscretization method for 3-dimensional motion of a Bingham fluid
    • Kim, J.U.: Semidiscretization method for 3-dimensional motion of a Bingham fluid. SIAM J. Math. Anal. 21, 53-75 (1990)
    • (1990) SIAM J. Math. Anal. , vol.21 , pp. 53-75
    • Kim, J.U.1
  • 47
    • 38249006533 scopus 로고
    • 2-Phase flow of Bingham fluids thorough porous-media
    • Kuang, P.Q., Kozicki, W.: 2-Phase flow of Bingham fluids thorough porous-media. Mech. Res. Commun. 16, 333-338 (1989)
    • (1989) Mech. Res. Commun. , vol.16 , pp. 333-338
    • Kuang, P.Q.1    Kozicki, W.2
  • 48
    • 0030158088 scopus 로고    scopus 로고
    • Evaluation of the flow rate of an electro-rheological fluid (corn starch kerosene) flowing through a narrow channel formed by a pair of electrodes
    • Kobayashi, K., Okamura, K., Sakai, T., Sato, M.: Evaluation of the flow rate of an electro-rheological fluid (corn starch kerosene) flowing through a narrow channel formed by a pair of electrodes. Canadian J. Chem. Eng. 74, 394-398 (1996)
    • (1996) Canadian J. Chem. Eng. , vol.74 , pp. 394-398
    • Kobayashi, K.1    Okamura, K.2    Sakai, T.3    Sato, M.4
  • 49
    • 0027224702 scopus 로고
    • Long waves in shallow-Water over a layer of Bingham-plastic fluid-mud. 1. Physical aspects
    • Liu, K.F., Mei, C.C.: Long waves in shallow-Water over a layer of Bingham-plastic fluid-mud. 1. Physical aspects. Int. J. Eng. Sci. 31, 125-144 (1993)
    • (1993) Int. J. Eng. Sci. , vol.31 , pp. 125-144
    • Liu, K.F.1    Mei, C.C.2
  • 50
    • 84968502760 scopus 로고
    • One-sided approximation and variational inequalities
    • Mosco, U., Strang, G.: One-sided approximation and variational inequalities. Bull. Am. Math. Soc. 80, 308-312 (1974)
    • (1974) Bull. Am. Math. Soc. , vol.80 , pp. 308-312
    • Mosco, U.1    Strang, G.2
  • 51
    • 0031277925 scopus 로고    scopus 로고
    • Theoretical study on equation of motion and yield stress of electrorheological fluid
    • Makihara, T., Tanahashi, T.: Theoretical study on equation of motion and yield stress of electrorheological fluid. JSME Int. J. Ser. B 40, 521-528 (1997)
    • (1997) JSME Int. J. Ser. B , vol.40 , pp. 521-528
    • Makihara, T.1    Tanahashi, T.2
  • 53
    • 0001183990 scopus 로고
    • ∞-Error Estimates for Semilinear Elliptic Problems with Free Boundaries
    • ∞-Error Estimates for Semilinear Elliptic Problems with Free Boundaries. Numer. Math. 54, 243-255 (1988)
    • (1988) Numer. Math. , vol.54 , pp. 243-255
    • Nochetto, R.H.1
  • 56
    • 0001779231 scopus 로고    scopus 로고
    • Error analysis for implicit approximations to solutions to Cauchy problems
    • Rulla, J.: Error analysis for implicit approximations to solutions to Cauchy problems. SIAM J. Numer. Anal. 33, 68-87 (1996)
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 68-87
    • Rulla, J.1
  • 57
    • 0032138419 scopus 로고    scopus 로고
    • Application of a flrst-oder operator splitting method to Bingham fluid flow simulation
    • Sanchez, F.J.: Application of a flrst-oder operator splitting method to Bingham fluid flow simulation. Comput. Math. Appl. 36, 71-86 (1998)
    • (1998) Comput. Math. Appl. , vol.36 , pp. 71-86
    • Sanchez, F.J.1
  • 58
    • 0000616291 scopus 로고    scopus 로고
    • Weak solutions and maximal regularity for abstract evolution inequalities
    • Savaré, G.: Weak solutions and maximal regularity for abstract evolution inequalities. Advances Math. Sc. Appl. 6, 377-418 (1996)
    • (1996) Advances Math. Sc. Appl. , vol.6 , pp. 377-418
    • Savaré, G.1
  • 59
    • 0000510362 scopus 로고
    • Numerical solution of the obstacle problem by the penalty method (Time-dependent problems)
    • Scholz, R.: Numerical solution of the obstacle problem by the penalty method (Time-dependent problems). Numer. Math 49, 255-268 (1986)
    • (1986) Numer. Math , vol.49 , pp. 255-268
    • Scholz, R.1
  • 60
    • 0021302113 scopus 로고
    • Numerical solution of the obstacle problem by the penalty method
    • Scholz, R.: Numerical solution of the obstacle problem by the penalty method. Computing 32, 297-306 (1984)
    • (1984) Computing , vol.32 , pp. 297-306
    • Scholz, R.1
  • 61
    • 21844492145 scopus 로고
    • Error estimates for the approximation of semicoercive variational inequalities
    • Spann, W.: Error estimates for the approximation of semicoercive variational inequalities. Numer. Math. 69, 103-116 (1994)
    • (1994) Numer. Math. , vol.69 , pp. 103-116
    • Spann, W.1
  • 63
    • 0042752993 scopus 로고
    • 2-Error estimate for an approximation of the solution of a parabolic variational inequality
    • 2-Error estimate for an approximation of the solution of a parabolic variational inequality. Numer. Math. 57, 453-471 (1990)
    • (1990) Numer. Math. , vol.57 , pp. 453-471
    • Vuik, C.1
  • 64
    • 0031618732 scopus 로고    scopus 로고
    • Rheology of cohesive sediments: Comparison between a natural and an artificial mud
    • Van Kessel, T., Blom, C.: Rheology of cohesive sediments: comparison between a natural and an artificial mud. J. Hydraulic Research 36, 591-612 (1998)
    • (1998) J. Hydraulic Research , vol.36 , pp. 591-612
    • Van Kessel, T.1    Blom, C.2
  • 65
    • 0031640703 scopus 로고    scopus 로고
    • Strongly coupled block-implicit solution technique for non-Newtonian convective heat transfer problems
    • Vradis, G.C., Hammand, K.J.: Strongly coupled block-implicit solution technique for non-Newtonian convective heat transfer problems. Numer. Heat Transfer Pt. B-fund. 33, 79-97 (1998)
    • (1998) Numer. Heat Transfer Pt. B-fund. , vol.33 , pp. 79-97
    • Vradis, G.C.1    Hammand, K.J.2
  • 66
    • 0342594643 scopus 로고
    • Heat-transfer in flows of non-Newtonian Bingham fluids through axisymmetrical sudden expansions and contractions
    • Vradis, G.C., Hammand, K.J.: Heat-transfer in flows of non-Newtonian Bingham fluids through axisymmetrical sudden expansions and contractions. Numer. Heat Transfer Pt. A-appl. 28, 339-353 (1995)
    • (1995) Numer. Heat Transfer Pt. A-appl. , vol.28 , pp. 339-353
    • Vradis, G.C.1    Hammand, K.J.2
  • 67
    • 0027333983 scopus 로고
    • Macroscopic conductivities for flow of Bingham plastics in porous-media
    • Vradis, G.C., Protopapas, A.L.: Macroscopic conductivities for flow of Bingham plastics in porous-media. J. Hydraul. Eng.-Asce 119, 95-108 (1993)
    • (1993) J. Hydraul. Eng.-asce , vol.119 , pp. 95-108
    • Vradis, G.C.1    Protopapas, A.L.2
  • 68
    • 0043263954 scopus 로고    scopus 로고
    • A numerical method for simulating non-Newtonian fluid flow and displacement in porous media
    • Wu, Y.S., Pruess, K.: A numerical method for simulating non-Newtonian fluid flow and displacement in porous media. Adv. Water Resour. 21, 351-362 (1998)
    • (1998) Adv. Water Resour. , vol.21 , pp. 351-362
    • Wu, Y.S.1    Pruess, K.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.