메뉴 건너뛰기




Volumn 150, Issue 1-4, 1997, Pages 397-409

Applications and numerical analysis of partial differential Volterra equations: A brief survey

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; ERROR ANALYSIS; FINITE ELEMENT METHOD; PROBLEM SOLVING;

EID: 0031337669     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(97)00077-7     Document Type: Article
Times cited : (16)

References (77)
  • 1
    • 0012517486 scopus 로고
    • A posteriori error estimation in finite element analysis
    • Technical report, University of Leicester Tech. Rep. 1995/14
    • M. Ainsworth and J.T. Oden, A posteriori error estimation in finite element analysis, Technical report, University of Leicester (Math. Comput. Sci.), 1995. Tech. Rep. 1995/14.
    • (1995) Math. Comput. Sci.
    • Ainsworth, M.1    Oden, J.T.2
  • 2
    • 0026189980 scopus 로고
    • Constitutive modelling and computation of non-linear viscoelastic solids. Part I: Theological models and numerical integration techniques
    • J. Argyris, I.St. Doltsinis and V.D. da Silva, Constitutive modelling and computation of non-linear viscoelastic solids. Part I: Theological models and numerical integration techniques, Comput. Methods Appl. Mech. Engrg. 88 (1991) 135-163.
    • (1991) Comput. Methods Appl. Mech. Engrg. , vol.88 , pp. 135-163
    • Argyris, J.1    Doltsinis, I.St.2    Da Silva, V.D.3
  • 3
    • 84985305586 scopus 로고
    • The h-p version of the finite element method for parabolic equations. Part II: The h-p version in time
    • I. Babuška and T. Janik, The h-p version of the finite element method for parabolic equations. Part II: the h-p version in time, Numer. Methods Partial Diff. Eqns. 6 (1990) 343-369.
    • (1990) Numer. Methods Partial Diff. Eqns. , vol.6 , pp. 343-369
    • Babuška, I.1    Janik, T.2
  • 4
    • 0016994245 scopus 로고
    • Error estimates for finite element methods for second order hyperbolic equations
    • G.A. Baker, Error estimates for finite element methods for second order hyperbolic equations, SIAM J. Numer. Anal. 13 (1976) 564-576.
    • (1976) SIAM J. Numer. Anal. , vol.13 , pp. 564-576
    • Baker, G.A.1
  • 5
    • 0024136590 scopus 로고
    • Solution of an equation for creep in solid polymers
    • J.T. Bendler, B. Noble and M.A. Hussain, Solution of an equation for creep in solid polymers, in: Proc. Computers in Engineering, number 3 in 1 (1988) 365-368.
    • (1988) Proc. Computers in Engineering , vol.3 , Issue.1 , pp. 365-368
    • Bendler, J.T.1    Noble, B.2    Hussain, M.A.3
  • 6
    • 0001178161 scopus 로고
    • The numerical solution of nonlinear Volterra integral equations of the second kind by collocation and iterated collocation methods
    • J.G. Blom and H. Brunner, The numerical solution of nonlinear Volterra integral equations of the second kind by collocation and iterated collocation methods, SIAM J. Sci. Stat. Comput. 8 (1987) 806-830.
    • (1987) SIAM J. Sci. Stat. Comput. , vol.8 , pp. 806-830
    • Blom, J.G.1    Brunner, H.2
  • 8
    • 0042251646 scopus 로고
    • On the numerical solution of nonlinear Volterra integro-differential equations
    • H. Brunner, On the numerical solution of nonlinear Volterra integro-differential equations, BIT 13 (1973) 381-390.
    • (1973) BIT , vol.13 , pp. 381-390
    • Brunner, H.1
  • 9
    • 84968521907 scopus 로고
    • Implicit Runge-Kutta methods of optimal order for Volterra integro-differential equations
    • H. Brunner, Implicit Runge-Kutta methods of optimal order for Volterra integro-differential equations, Math. Comput. 42 (1984) 95-109.
    • (1984) Math. Comput. , vol.42 , pp. 95-109
    • Brunner, H.1
  • 10
    • 0021552066 scopus 로고
    • Iterated collocation methods and their discretizations for Volterra integral equations
    • H. Brunner, Iterated collocation methods and their discretizations for Volterra integral equations, SIAM J. Numer. Anal 21 (1984) 1132-1145.
    • (1984) SIAM J. Numer. Anal , vol.21 , pp. 1132-1145
    • Brunner, H.1
  • 11
    • 84968503497 scopus 로고
    • Collocation methods for nonlinear Volterra integro-differential equations with infinite delay
    • H. Brunner, Collocation methods for nonlinear Volterra integro-differential equations with infinite delay, Math. Comput. 53 (1989) 571-587.
    • (1989) Math. Comput. , vol.53 , pp. 571-587
    • Brunner, H.1
  • 12
    • 0025477912 scopus 로고
    • On the numerical solution of nonlinear Volterra-Fredholm integral equations by collocation methods
    • H. Brunner, On the numerical solution of nonlinear Volterra-Fredholm integral equations by collocation methods, SIAM J. Numer. Anal. 27 (1990) 987-1000.
    • (1990) SIAM J. Numer. Anal. , vol.27 , pp. 987-1000
    • Brunner, H.1
  • 13
    • 84966198465 scopus 로고
    • Runge-Kutta theory for Volterra integral equations of the second kind
    • H. Brunner, E. Hairer and S.P. Nørsett, Runge-Kutta theory for Volterra integral equations of the second kind, Math. Comput. 39 (1982) 147-163.
    • (1982) Math. Comput. , vol.39 , pp. 147-163
    • Brunner, H.1    Hairer, E.2    Nørsett, S.P.3
  • 14
    • 0019632810 scopus 로고
    • The direct numerical solution of a Volterra integral equation arising out of viscoelastic stress in materials
    • R.F. Cameron and S. McKee, The direct numerical solution of a Volterra integral equation arising out of viscoelastic stress in materials, Comput. Methods Appl. Mech. Engrg. 29 (1981) 219-232.
    • (1981) Comput. Methods Appl. Mech. Engrg. , vol.29 , pp. 219-232
    • Cameron, R.F.1    McKee, S.2
  • 15
    • 51249176168 scopus 로고
    • 1 projection and Galerkin methods for non-linear parabolic integro-differential equations
    • 1 projection and Galerkin methods for non-linear parabolic integro-differential equations, Calcolo 25 (1988) 187-201.
    • (1988) Calcolo , vol.25 , pp. 187-201
    • Cannon, J.R.1    Lin, Y.2
  • 16
    • 0025445438 scopus 로고
    • 2 error estimates for finite-element methods for nonlinear diffusion equations with memory
    • 2 error estimates for finite-element methods for nonlinear diffusion equations with memory, SIAM J. Numer. Anal. 27 (1990) 595-607.
    • (1990) SIAM J. Numer. Anal. , vol.27 , pp. 595-607
    • Cannon, J.R.1    Lin, Y.2
  • 19
    • 0026138684 scopus 로고
    • Sharp fronts due to diffusion and viscoelastic relaxation in polymers
    • D.S. Cohen and A.B. White Jr., Sharp fronts due to diffusion and viscoelastic relaxation in polymers, SIAM J. Appl. Math. 51 (1991) 472-483.
    • (1991) SIAM J. Appl. Math. , vol.51 , pp. 472-483
    • Cohen, D.S.1    White A.B., Jr.2
  • 20
    • 0029287710 scopus 로고
    • Shock formation in a multidimensional viscoelastic diffusive system
    • D.S. Cohen, A.B. White Jr. and T.P. Witelski, Shock formation in a multidimensional viscoelastic diffusive system, SIAM J. Appl. Math. 55 (1995) 348-368.
    • (1995) SIAM J. Appl. Math. , vol.55 , pp. 348-368
    • Cohen, D.S.1    White A.B., Jr.2    Witelski, T.P.3
  • 21
    • 0000906473 scopus 로고
    • Foundations of linear viscoelasticity
    • B.D. Coleman and W. Noll, Foundations of linear viscoelasticity, Rev. Modern Phys. 33 (1961) 239-249.
    • (1961) Rev. Modern Phys. , vol.33 , pp. 239-249
    • Coleman, B.D.1    Noll, W.2
  • 22
    • 25644446425 scopus 로고
    • Some equations modelling growth processes and gonorrhea epidemics
    • K.L. Cooke and J.A. Yorke, Some equations modelling growth processes and gonorrhea epidemics, Math. Biosci. 16 (1973) 75-101.
    • (1973) Math. Biosci. , vol.16 , pp. 75-101
    • Cooke, K.L.1    Yorke, J.A.2
  • 23
    • 84966254473 scopus 로고
    • Discontinuous Galerkin methods for ordinary differential equations
    • M. Delfour, W. Hager and F. Trochu, Discontinuous Galerkin methods for ordinary differential equations, Math. Comput. 36 (1981) 455-473.
    • (1981) Math. Comput. , vol.36 , pp. 455-473
    • Delfour, M.1    Hager, W.2    Trochu, F.3
  • 24
    • 0040581478 scopus 로고
    • Repeated integral inequalities
    • J. Dixon and S. McKee, Repeated integral inequalities, IMA J. Numer. Anal. 4 (1984) 99-107.
    • (1984) IMA J. Numer. Anal. , vol.4 , pp. 99-107
    • Dixon, J.1    McKee, S.2
  • 25
    • 0042285018 scopus 로고
    • A unified approach to convergence analysis of discretization methods for Volterra-type equations
    • J. Dixon and S. McKee, A unified approach to convergence analysis of discretization methods for Volterra-type equations, IMA J. Numer. Anal. 5 (1985) 41-57.
    • (1985) IMA J. Numer. Anal. , vol.5 , pp. 41-57
    • Dixon, J.1    McKee, S.2
  • 26
    • 34250973096 scopus 로고
    • Numerical methods for integro-differential equations of parabolic and hyperbolic types
    • J. Douglas and B.F. Jones, Numerical methods for integro-differential equations of parabolic and hyperbolic types, Numer. Math. 4 (1962) 96-102.
    • (1962) Numer. Math. , vol.4 , pp. 96-102
    • Douglas, J.1    Jones, B.F.2
  • 27
    • 0000807980 scopus 로고
    • 2-estimates for Galerkin methods for second order hyperbolic equations
    • 2-estimates for Galerkin methods for second order hyperbolic equations, SIAM J. Numer. Anal. 10 (1973) 880-889.
    • (1973) SIAM J. Numer. Anal. , vol.10 , pp. 880-889
    • Dupont, T.1
  • 28
    • 84966225938 scopus 로고
    • An adaptive finite element method for linear elliptic problems
    • K. Eriksson and C. Johnson, An adaptive finite element method for linear elliptic problems, Math. Comput. 50 (1988) 361-383.
    • (1988) Math. Comput. , vol.50 , pp. 361-383
    • Eriksson, K.1    Johnson, C.2
  • 29
    • 0026106415 scopus 로고
    • Adaptive finite element methods for parabolic problems. I: A linear model problem
    • K. Erikkson and C. Johnson, Adaptive finite element methods for parabolic problems. I: A linear model problem, SIAM J. Numer. Anal. 28 (1991) 43-77.
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 43-77
    • Erikkson, K.1    Johnson, C.2
  • 30
    • 0001164460 scopus 로고
    • A posteriori error bounds and global error control for approximation of ordinary differential equations
    • D. Estep, A posteriori error bounds and global error control for approximation of ordinary differential equations, SIAM J. Numer. Anal. 32 (1995) 1-48.
    • (1995) SIAM J. Numer. Anal. , vol.32 , pp. 1-48
    • Estep, D.1
  • 31
    • 0042285017 scopus 로고
    • Multistep multiderivative methods for Volterra integro-differential equations
    • M. Favaro, S. McKee and M. Meneguette, Multistep multiderivative methods for Volterra integro-differential equations, Int. J. Comput. Math. 22 (1987) 161-175.
    • (1987) Int. J. Comput. Math. , vol.22 , pp. 161-175
    • Favaro, M.1    McKee, S.2    Meneguette, M.3
  • 34
    • 0001287486 scopus 로고
    • Fast numerical solution of nonlinear Volterra convolution equations
    • E. Hairer, CH. Lubich and M. Schlichte, Fast numerical solution of nonlinear Volterra convolution equations, SIAM J. Sci. Stat. Comput. 6 (1985) 532-541.
    • (1985) SIAM J. Sci. Stat. Comput. , vol.6 , pp. 532-541
    • Hairer, E.1    Lubich, Ch.2    Schlichte, M.3
  • 36
    • 84968493695 scopus 로고
    • Discrete Galerkin and related one-step methods for ordinary differential equations
    • B.L. Hulme, Discrete Galerkin and related one-step methods for ordinary differential equations, Math. Comput. 26 (1972) 881-891.
    • (1972) Math. Comput. , vol.26 , pp. 881-891
    • Hulme, B.L.1
  • 37
    • 0002298440 scopus 로고
    • Galerkin-type approximations which are discontinuous in time for parabolic equations in a variable domain
    • P. Jamet, Galerkin-type approximations which are discontinuous in time for parabolic equations in a variable domain, SIAM J. Numer. Anal. 15 (1978) 912-928.
    • (1978) SIAM J. Numer. Anal. , vol.15 , pp. 912-928
    • Jamet, P.1
  • 38
    • 0029395276 scopus 로고
    • Numerical methods for treating problems of viscoelastic isotropic solid deformation
    • V. Janovsky, S. Shaw, M.K. Warby and J.R. Whiteman, Numerical methods for treating problems of viscoelastic isotropic solid deformation, J. Comput. Appl. Math. 63 (1995) 91-107.
    • (1995) J. Comput. Appl. Math. , vol.63 , pp. 91-107
    • Janovsky, V.1    Shaw, S.2    Warby, M.K.3    Whiteman, J.R.4
  • 39
    • 0001562231 scopus 로고
    • Error estimates and adaptive time step control for a class of one step methods for stiff ordinary differential equations
    • C. Johnson, Error estimates and adaptive time step control for a class of one step methods for stiff ordinary differential equations, SIAM J. Numer. Anal. 25 (1988) 908-926.
    • (1988) SIAM J. Numer. Anal. , vol.25 , pp. 908-926
    • Johnson, C.1
  • 41
    • 0027004931 scopus 로고
    • Adaptive finite element methods in computational mechanics
    • C. Johnson and P. Hansbo, Adaptive finite element methods in computational mechanics, Comput. Methods Appl. Mech. Engrg. 101 (1992) 143-181.
    • (1992) Comput. Methods Appl. Mech. Engrg. , vol.101 , pp. 143-181
    • Johnson, C.1    Hansbo, P.2
  • 42
    • 84966251039 scopus 로고
    • Variable step size predictor-corrector schemes for second kind Volterra integral equations
    • H.M. Jones and S. McKee, Variable step size predictor-corrector schemes for second kind Volterra integral equations, Math. Comput. 44 (1985) 391-404.
    • (1985) Math. Comput. , vol.44 , pp. 391-404
    • Jones, H.M.1    McKee, S.2
  • 44
    • 0019279481 scopus 로고
    • Non-linear viscoelasticity based on free volume consideration
    • W.G. Knauss and I.J. Emri, Non-linear viscoelasticity based on free volume consideration, Comput. Struct. 13 (1981) 123-128.
    • (1981) Comput. Struct. , vol.13 , pp. 123-128
    • Knauss, W.G.1    Emri, I.J.2
  • 45
    • 0025447066 scopus 로고
    • Galerkin methods for nonlinear parabolic integrodifferential equations with nonlinear boundary conditions
    • Y. Lin, Galerkin methods for nonlinear parabolic integrodifferential equations with nonlinear boundary conditions, SIAM J. Numer. Anal. 27 (1990) 608-621.
    • (1990) SIAM J. Numer. Anal. , vol.27 , pp. 608-621
    • Lin, Y.1
  • 46
    • 0026204786 scopus 로고
    • Ritz-Volterra projections to finite-element spaces and applications to integrodifferential and related equations
    • Y. Lin, V. Thomée and L.B. Wahlbin, Ritz-Volterra projections to finite-element spaces and applications to integrodifferential and related equations, SIAM J. Numer. Anal. 28 (1991) 1047-1070.
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 1047-1070
    • Lin, Y.1    Thomée, V.2    Wahlbin, L.B.3
  • 48
    • 0021377643 scopus 로고
    • Lax-Wendroff methods for hyperbolic history value problems
    • P. Markowich and M. Renardy, Lax-Wendroff methods for hyperbolic history value problems, SIAM J. Numer. Anal. 21 (1984) 24-51.
    • (1984) SIAM J. Numer. Anal. , vol.21 , pp. 24-51
    • Markowich, P.1    Renardy, M.2
  • 49
    • 0029269769 scopus 로고
    • A posteriori error estimates and adaptivity for finite element solutions in finite elasticity
    • R. Mücke and J.R. Whiteman, A posteriori error estimates and adaptivity for finite element solutions in finite elasticity, Int. J. Numer. Methods Engrg. 38 (1995) 775-795.
    • (1995) Int. J. Numer. Methods Engrg. , vol.38 , pp. 775-795
    • Mücke, R.1    Whiteman, J.R.2
  • 50
    • 0008849603 scopus 로고
    • On heat conduction in materials with memory
    • J.W. Nunziato, On heat conduction in materials with memory, Quart. Appl. Math. 29 (1971) 187-204.
    • (1971) Quart. Appl. Math. , vol.29 , pp. 187-204
    • Nunziato, J.W.1
  • 51
    • 0037827941 scopus 로고
    • Numerical methods for hyperbolic and parabolic integro-differential equations
    • A.K. Pani, V. Thomée and L.B. Wahlbin, Numerical methods for hyperbolic and parabolic integro-differential equations, J. Integral Eqns. Appl. 4 (1992) 533-584.
    • (1992) J. Integral Eqns. Appl. , vol.4 , pp. 533-584
    • Pani, A.K.1    Thomée, V.2    Wahlbin, L.B.3
  • 52
    • 0001669214 scopus 로고    scopus 로고
    • Finite element methods with numerical quadrature for parabolic integrodifferential equations
    • A.K. Pani and T.E. Peterson, Finite element methods with numerical quadrature for parabolic integrodifferential equations, SIAM J. Numer. Anal. 33 (1996) 1084-1105.
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 1084-1105
    • Pani, A.K.1    Peterson, T.E.2
  • 53
    • 0041197866 scopus 로고
    • Numerical solution of semilinear integrodifferential equations of parabolic type with nonsmooth data
    • M.-N. Le Roux and V. Thomée, Numerical solution of semilinear integrodifferential equations of parabolic type with nonsmooth data, SIAM J. Numer. Anal. 26 (1989) 1291-1309.
    • (1989) SIAM J. Numer. Anal. , vol.26 , pp. 1291-1309
    • Le Roux, M.-N.1    Thomée, V.2
  • 54
    • 0042284957 scopus 로고
    • On the exact order of convergence of discrete methods for Volterra-type equations
    • J. Scott and S. McKee, On the exact order of convergence of discrete methods for Volterra-type equations, IMA J. Numer. Anal. 8 (1988) 511-515.
    • (1988) IMA J. Numer. Anal. , vol.8 , pp. 511-515
    • Scott, J.1    McKee, S.2
  • 55
    • 0043287208 scopus 로고    scopus 로고
    • An implicit history discretization of a hereditary wave equation
    • P. Michavila, ed., Universidad Politecnica de Madrid, Expected
    • S. Shaw, M.K. Warby and J.R. Whiteman, An implicit history discretization of a hereditary wave equation, in: P. Michavila, ed., Seminario de Analisis Numerico, Universidad Politecnica de Madrid, Expected 1996.
    • (1996) Seminario de Analisis Numerico
    • Shaw, S.1    Warby, M.K.2    Whiteman, J.R.3
  • 57
    • 0030571236 scopus 로고    scopus 로고
    • Discrete schemes for treating hereditary problems of viscoelasticity and applications
    • S. Shaw, M.K. Warby and J.R. Whiteman, Discrete schemes for treating hereditary problems of viscoelasticity and applications, J. Comput. Appl. Math. 74 (1996) 313-329.
    • (1996) J. Comput. Appl. Math. , vol.74 , pp. 313-329
    • Shaw, S.1    Warby, M.K.2    Whiteman, J.R.3
  • 58
    • 0000823719 scopus 로고    scopus 로고
    • Error estimates with sharp constants for a fading memory Volterra problem in linear solid viscoelasticity
    • S. Shaw, M.K. Warby and J.R. Whiteman, Error estimates with sharp constants for a fading memory Volterra problem in linear solid viscoelasticity. To appear in SIAM J. Numer. Anal. 34 (1997) 1237-1254.
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 1237-1254
    • Shaw, S.1    Warby, M.K.2    Whiteman, J.R.3
  • 59
    • 0028531194 scopus 로고
    • Numerical techniques for the treatment of quasistatic viscoelastic stress problems in linear isotropic solids
    • S. Shaw, M.K. Warby, J.R. Whiteman, C. Dawson and M.F. Wheeler, Numerical techniques for the treatment of quasistatic viscoelastic stress problems in linear isotropic solids, Comput. Methods Appl. Mech. Engrg. 118 (1994) 211-237.
    • (1994) Comput. Methods Appl. Mech. Engrg. , vol.118 , pp. 211-237
    • Shaw, S.1    Warby, M.K.2    Whiteman, J.R.3    Dawson, C.4    Wheeler, M.F.5
  • 60
    • 0006352239 scopus 로고    scopus 로고
    • Backward Euler and Crank-Nicolson finite element variants with rational adaptivity and a posteriori error estimates for an integrodifferential equation
    • submitted
    • S. Shaw and J.R. Whiteman, Backward Euler and Crank-Nicolson finite element variants with rational adaptivity and a posteriori error estimates for an integrodifferential equation, Math. Comput. (1996) submitted.
    • (1996) Math. Comput.
    • Shaw, S.1    Whiteman, J.R.2
  • 61
    • 0030509131 scopus 로고    scopus 로고
    • i) error estimate for second-kind Volterra problems
    • i) error estimate for second-kind Volterra problems, Numer. Math. 74 (1996) 361-383.
    • (1996) Numer. Math. , vol.74 , pp. 361-383
    • Shaw, S.1    Whiteman, J.R.2
  • 62
    • 21444458718 scopus 로고    scopus 로고
    • Towards adaptive finite element schemes for partial differential Volterra equation solvers
    • S. Shaw and J.R. Whiteman, Towards adaptive finite element schemes for partial differential Volterra equation solvers. Adv. Comput. Math. 6 (1996) 309-323.
    • (1996) Adv. Comput. Math. , vol.6 , pp. 309-323
    • Shaw, S.1    Whiteman, J.R.2
  • 63
    • 0043287207 scopus 로고
    • Towards robust adaptive finite element methods for partial differential Volterra equation problems arising in viscoelasticity theory
    • J.R. Whiteman, ed., Wiley, Chichester
    • S. Shaw and J.R. Whiteman, Towards robust adaptive finite element methods for partial differential Volterra equation problems arising in viscoelasticity theory, in: J.R. Whiteman, ed., The Mathematics of Finite Elements and Applications. MAFELAP 1996 (Wiley, Chichester, 1977).
    • (1977) The Mathematics of Finite Elements and Applications. MAFELAP 1996
    • Shaw, S.1    Whiteman, J.R.2
  • 64
    • 0001406595 scopus 로고
    • Time discretization of an integro-differential equation of parabolic type
    • I.H. Sloan and V. Thomée, Time discretization of an integro-differential equation of parabolic type, SIAM J. Numer. Anal. 23 (1986) 1052-1061.
    • (1986) SIAM J. Numer. Anal. , vol.23 , pp. 1052-1061
    • Sloan, I.H.1    Thomée, V.2
  • 65
    • 0043287206 scopus 로고
    • A nonlinear model for human population dynamics
    • K.E. Swick, A nonlinear model for human population dynamics, DSIAM J. Appl. Math. 40 (1981) 266-278.
    • (1981) DSIAM J. Appl. Math. , vol.40 , pp. 266-278
    • Swick, K.E.1
  • 66
    • 84968518942 scopus 로고
    • Long-time numerical solution of a parabolic equation with memory
    • V. Thomée and L.B. Wahlbin, Long-time numerical solution of a parabolic equation with memory, Math. Comput. 62 (1994) 477-496.
    • (1994) Math. Comput. , vol.62 , pp. 477-496
    • Thomée, V.1    Wahlbin, L.B.2
  • 68
    • 0026870293 scopus 로고
    • A finite element model of crack growth in a finite body in the context of mode I linear viscoelastic fracture
    • M.K. Warby, J.R. Walton and J.R. Whiteman, A finite element model of crack growth in a finite body in the context of mode I linear viscoelastic fracture, Comput. Methods Appl. Mech. Engrg. 97 (1992) 375-397.
    • (1992) Comput. Methods Appl. Mech. Engrg. , vol.97 , pp. 375-397
    • Warby, M.K.1    Walton, J.R.2    Whiteman, J.R.3
  • 69
    • 0042284955 scopus 로고
    • The computational modelling of thermoforming for the creation axisymmetric container structures
    • M. Cross, J.F.T. Pittman and R.D. Wood, eds., Clarendon Press, Oxford
    • M.K. Warby and J.R. Whiteman, The computational modelling of thermoforming for the creation axisymmetric container structures, in: M. Cross, J.F.T. Pittman and R.D. Wood, eds., Mathematical Modelling for Materials Processing (Clarendon Press, Oxford, 1993) 159-175.
    • (1993) Mathematical Modelling for Materials Processing , pp. 159-175
    • Warby, M.K.1    Whiteman, J.R.2
  • 70
    • 0001287713 scopus 로고
    • 2 error estimates for Galerkin approximations to parabolic partial differential equations
    • 2 error estimates for Galerkin approximations to parabolic partial differential equations, SIAM J. Numer. Anal. 10 (1973) 723-759.
    • (1973) SIAM J. Numer. Anal. , vol.10 , pp. 723-759
    • Wheeler, M.F.1
  • 72
    • 0003397355 scopus 로고
    • A survey of gradient superconvergence for finite element approximations to second order elliptic problems on triangular and tetrahedral meshes
    • J.R. Whiteman, ed., Academic Press, London
    • J.R. Whiteman and G. Goodsell, A survey of gradient superconvergence for finite element approximations to second order elliptic problems on triangular and tetrahedral meshes, in: J.R. Whiteman, ed., The Mathematics of Finite Elements and Applications. MAFELAP 1990 (Academic Press, London, 1991).
    • (1991) The Mathematics of Finite Elements and Applications. MAFELAP 1990
    • Whiteman, J.R.1    Goodsell, G.2
  • 73
    • 0005718021 scopus 로고
    • Finite element methods for parabolic and hyperbolic partial integro-ditterential equations
    • E.G. Yanik and G. Fairweather, Finite element methods for parabolic and hyperbolic partial integro-ditterential equations, Nonlinear Anal., Theory, Methods Applic. 12 (1988) 785-809.
    • (1988) Nonlinear Anal., Theory, Methods Applic. , vol.12 , pp. 785-809
    • Yanik, E.G.1    Fairweather, G.2
  • 74
    • 0025516996 scopus 로고
    • Superconvergence recovery technique and a posteriori error estimators
    • J.Z. Zhu and O.C. Zienkiewicz, Superconvergence recovery technique and a posteriori error estimators, Int. J. Numer. Methods Engrg. 30 (1990) 1321-1339.
    • (1990) Int. J. Numer. Methods Engrg. , vol.30 , pp. 1321-1339
    • Zhu, J.Z.1    Zienkiewicz, O.C.2
  • 76
    • 0004621370 scopus 로고
    • Some creep effects in stress analysis with particular reference to concrete pressure vessels
    • O.C. Zienkiewicz and M. Watson, Some creep effects in stress analysis with particular reference to concrete pressure vessels, Nucl. Engrg. Des. 4 (1966) 406-412.
    • (1966) Nucl. Engrg. Des. , vol.4 , pp. 406-412
    • Zienkiewicz, O.C.1    Watson, M.2
  • 77
    • 0026869285 scopus 로고
    • The superconvergent patch recovery and a posteriori error estimates. Part 2: Error estimates and adaptivity
    • O.C. Zienkiewicz and J.Z. Zhu, The superconvergent patch recovery and a posteriori error estimates. Part 2: Error estimates and adaptivity, Int. J. Numer. Methods Engrg. 33 (1992) 1365-1382.
    • (1992) Int. J. Numer. Methods Engrg. , vol.33 , pp. 1365-1382
    • Zienkiewicz, O.C.1    Zhu, J.Z.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.