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Volumn 15, Issue 2, 1997, Pages 159-178

On maximum norm estimates for Ritz-Volterra projection with applications to some time dependent problems

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EID: 0042742929     PISSN: 02549409     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (24)

References (28)
  • 1
    • 0000425575 scopus 로고
    • Some convergence estimates for semidiscrete Galerkin type approximations for parabolic equations
    • J.H. Bramble, A.H. Schatz, V. Thomee and L.B. Wahlbin, Some convergence estimates for semidiscrete Galerkin type approximations for parabolic equations, SIAM J. Numer. Anal., 14(1977), 218-241.
    • (1977) SIAM J. Numer. Anal. , vol.14 , pp. 218-241
    • Bramble, J.H.1    Schatz, A.H.2    Thomee, V.3    Wahlbin, L.B.4
  • 2
    • 0023364649 scopus 로고
    • A Galerkin procedure for the diffusion equation subject to the specification of mass
    • J.R. Cannon, S. Perez-Esteva and J. van der Hoek, A Galerkin procedure for the diffusion equation subject to the specification of mass, SIAM J. Numer. Anal., 24(1987), 499-515.
    • (1987) SIAM J. Numer. Anal. , vol.24 , pp. 499-515
    • Cannon, J.R.1    Perez-Esteva, S.2    Van Der Hoek, J.3
  • 3
    • 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), 505-607.
    • (1990) SIAM J. Numer. Anal. , vol.27 , pp. 505-607
    • Cannon, J.R.1    Lin, Y.2
  • 4
    • 51249176168 scopus 로고
    • 1 projection and Galerkin methods for nonlinear parabolic integro-differential equation
    • 1 projection and Galerkin methods for nonlinear parabolic integro-differential equation, Calcolo, 25(1988), 187-201.
    • (1988) Calcolo , vol.25 , pp. 187-201
    • Cannon, J.R.1    Lin, Y.2
  • 5
    • 0025535884 scopus 로고
    • A Galerkin procedure for diffusion equations with boundary integral conditions
    • R. Cannon and Y. Lin, A Galerkin procedure for diffusion equations with boundary integral conditions, Int. J. Eng. sci., 28(1990), 579-587.
    • (1990) Int. J. Eng. Sci. , vol.28 , pp. 579-587
    • Cannon, R.1    Lin, Y.2
  • 8
    • 0040138359 scopus 로고
    • Galerkin methods for parabolic equations with nonlinear boundary conditions
    • J. Douglas, Jr. and T. Dupont, Galerkin methods for parabolic equations with nonlinear boundary conditions, Numer. Math., 20(1973), 213-237.
    • (1973) Numer. Math. , vol.20 , pp. 213-237
    • Douglas Jr., J.1    Dupont, T.2
  • 9
    • 84966225382 scopus 로고
    • Sharp Maximun norm error estimates for finite element approximations of the Stokes problem in 2-D
    • R. Duran, R. Nochetto and J. Wang, Sharp Maximun norm error estimates for finite element approximations of the Stokes problem in 2-D, Math. Comp., 15(1988), 491-506.
    • (1988) Math. Comp. , vol.15 , pp. 491-506
    • Duran, R.1    Nochetto, R.2    Wang, J.3
  • 10
    • 0002230465 scopus 로고
    • 1-Fehlerabschätzung für diskrete Grundlösungen in der Methode der finiten Elemente
    • 1-Fehlerabschätzung für diskrete Grundlösungen in der Methode der finiten Elemente, Bonner Math. Schriften, 89(1976), 92-114.
    • (1976) Bonner Math. Schriften , vol.89 , pp. 92-114
    • Frehse, J.1    Rannacher, R.2
  • 11
    • 0005718021 scopus 로고
    • Finite element methods for parabolic and hyperbolic partial integro-differential equations
    • E. Greenwell Yanik and G. Fairweather, Finite element methods for parabolic and hyperbolic partial integro-differential equations, Nonlinear Analysis, 12(1988), 785-809.
    • (1988) Nonlinear Analysis , vol.12 , pp. 785-809
    • Greenwell Yanik, E.1    Fairweather, G.2
  • 12
    • 0041197866 scopus 로고
    • Numerical solution of semilinear integro-differential equations of parabolic type with nonsmooth data
    • M.N. LeRoux and V. Thomee, Numerical solution of semilinear integro-differential 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
    • Leroux, M.N.1    Thomee, V.2
  • 13
    • 0025447066 scopus 로고
    • Galerkin methods for nonlinear parabolic integro-differential equations with nonlinear boundary conditions
    • Y. Lin, Galerkin methods for nonlinear parabolic integro-differential equations with nonlinear boundary conditions, SIAM J. Numer. Anal., SIAM J. Numer. Anal., 27(1990), 608-621.
    • (1990) SIAM J. Numer. Anal., SIAM J. Numer. Anal. , vol.27 , pp. 608-621
    • Lin, Y.1
  • 14
    • 0026204786 scopus 로고
    • Ritz-Volterra projection onto finite element spaces and applications to integro-differential and related equations
    • Y. Lin, V. Thomee and L. Wahlbin, Ritz-Volterra projection onto finite element spaces and applications to integro-differential and related equations, SIAM J. Numer. Anal., 28(1991), 1047-1070.
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 1047-1070
    • Lin, Y.1    Thomee, V.2    Wahlbin, L.3
  • 15
    • 0011854764 scopus 로고
    • The stability of Ritz-Volterra projection and error estimatyes for finite element methods for a class of integro-differential equations of parabolic type
    • Y. Lin and T. Zhang, The stability of Ritz-Volterra projection and error estimatyes for finite element methods for a class of integro-differential equations of parabolic type, Appl. Mat., 36(1991), 123-133.
    • (1991) Appl. Mat. , vol.36 , pp. 123-133
    • Lin, Y.1    Zhang, T.2
  • 16
    • 34250381303 scopus 로고
    • Über der punktweise Konvergenz finiter Elemente
    • F. Natterer, Über der punktweise Konvergenz finiter Elemente, Numer. Math., 25(1975), 67-78.
    • (1975) Numer. Math. , vol.25 , pp. 67-78
    • Natterer, F.1
  • 17
    • 0001175292 scopus 로고
    • ∞-convergence of finite element approximations, Mathematical Aspects of Finite Element Methods
    • Springer-verlag, New York
    • ∞-convergence of finite element approximations, Mathematical Aspects of Finite Element Methods, Lecture Note in Mathematics, Vol.606, Springer-verlag, New York, 1977.
    • (1977) Lecture Note in Mathematics , vol.606
    • Nitsche, J.A.1
  • 18
    • 84968491183 scopus 로고
    • Some optimal error estimates for piecewise linear finite element approximations
    • R. Rannacher and R. Scott, Some optimal error estimates for piecewise linear finite element approximations, Math. Comp., 38(1982), 1-22.
    • (1982) Math. Comp. , vol.38 , pp. 1-22
    • Rannacher, R.1    Scott, R.2
  • 19
    • 33746187872 scopus 로고
    • An Analysis of the Finite Element Method for Second Order Elliptic Boundary Value Problems
    • Math. Dept., Cornell University
    • A.H. Schatz, An Analysis of the Finite Element Method for Second Order Elliptic Boundary Value Problems, Lecture Notes, Math. Dept., Cornell University, 1988.
    • (1988) Lecture Notes
    • Schatz, A.H.1
  • 20
    • 84966241381 scopus 로고
    • Interior maximum norm estimates for finite element methods
    • A.H. Schatz and L.B. Wahlbin, Interior maximum norm estimates for finite element methods. Math. Comp., 31(1976), 414-442.
    • (1976) Math. Comp. , vol.31 , pp. 414-442
    • Schatz, A.H.1    Wahlbin, L.B.2
  • 21
    • 84980170637 scopus 로고
    • Maximum norm stability and error estimates in parabolic finite element equations
    • A.H. Schatz, V. Thomee and L. Wahlbin, Maximum norm stability and error estimates in parabolic finite element equations, Commun. Pure. Appl. Math., 33(1980), 265-304.
    • (1980) Commun. Pure. Appl. Math. , vol.33 , pp. 265-304
    • Schatz, A.H.1    Thomee, V.2    Wahlbin, L.3
  • 22
    • 84966250424 scopus 로고
    • ∞ estimates for the finite element methods on irregular meshes
    • ∞ estimates for the finite element methods on irregular meshes, Math. Comp., 30(1976), 681-697.
    • (1976) Math. Comp. , vol.30 , pp. 681-697
    • Scott, R.1
  • 23
    • 0001406595 scopus 로고
    • Time discretization of an integro-differential equation of parabolic type
    • I.H. Sloan and V. Thomee, 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    Thomee, V.2
  • 24
    • 0003208045 scopus 로고
    • Galerkin Finite Element Methods for Parabolic Problems
    • Springer-Verlag
    • V. Thomee, Galerkin Finite Element Methods for Parabolic Problems, Lecture Notes in Mathematics, 1054, Springer-Verlag, 1984.
    • (1984) Lecture Notes in Mathematics , vol.1054
    • Thomee, V.1
  • 25
    • 0012969770 scopus 로고
    • Maximum-norm stability and error estimates in Galerkin methods for parabolic equations in one space variable
    • V. Thomee and L.B. Wahlbin, Maximum-norm stability and error estimates in Galerkin methods for parabolic equations in one space variable, Numer. Math., 41(1983), 345-371.
    • (1983) Numer. Math. , vol.41 , pp. 345-371
    • Thomee, V.1    Wahlbin, L.B.2
  • 26
    • 84968515653 scopus 로고
    • Error estimates for semi-discrete finite element methods for parabolic integro-differential equations
    • V. Thomee and N.Y. Zhang, Error estimates for semi-discrete finite element methods for parabolic integro-differential equations, Math. Comp., 53(1989), 121-139.
    • (1989) Math. Comp. , vol.53 , pp. 121-139
    • Thomee, V.1    Zhang, N.Y.2
  • 27
    • 0040586155 scopus 로고
    • ∞-error estimates for mixed finite element methods for second order elliptic problems
    • ∞-error estimates for mixed finite element methods for second order elliptic problems, Numer. Math., 55(1989), 401-430.
    • (1989) Numer. Math. , vol.55 , pp. 401-430
    • Wang, J.1
  • 28
    • 0001287713 scopus 로고
    • 2 error estimates for Galerkin approximation to parabolic partial differential equations
    • 2 error estimates for Galerkin approximation to parabolic partial differential equations, SIAM J. Numer. Anal., 19(1973), 72.
    • (1973) SIAM J. Numer. Anal. , vol.19 , pp. 72
    • Wheeler, M.F.1


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