메뉴 건너뛰기




Volumn 196, Issue 35-36, 2007, Pages 3462-3474

A posteriori error estimates for fully discrete nonlinear parabolic problems

Author keywords

A posteriori error estimation; Finite element method; Nonlinear parabolic equations

Indexed keywords

APPROXIMATION THEORY; CONTINUOUS TIME SYSTEMS; FINITE ELEMENT METHOD; GALERKIN METHODS; NONLINEAR EQUATIONS;

EID: 34250370355     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2007.03.015     Document Type: Article
Times cited : (18)

References (28)
  • 1
    • 0003796630 scopus 로고
    • Academic Press, New York
    • Adams R. Sobolev Spaces (1975), Academic Press, New York
    • (1975) Sobolev Spaces
    • Adams, R.1
  • 2
    • 0033293882 scopus 로고    scopus 로고
    • A posteriori finite element error estimation for diffusion problems
    • Adjerid S., Belguendouz B., and Flaherty J.E. A posteriori finite element error estimation for diffusion problems. SIAM J. Sci. Comput. 21 (1999) 728-746
    • (1999) SIAM J. Sci. Comput. , vol.21 , pp. 728-746
    • Adjerid, S.1    Belguendouz, B.2    Flaherty, J.E.3
  • 4
    • 33745448006 scopus 로고    scopus 로고
    • The postprocessed mixed finite-element method for the Navier-Stokes equations
    • Ayuso B., García-Archilla B., and Novo J. The postprocessed mixed finite-element method for the Navier-Stokes equations. SIAM J. Numer. Anal. 43 (2005) 1091-1111
    • (2005) SIAM J. Numer. Anal. , vol.43 , pp. 1091-1111
    • Ayuso, B.1    García-Archilla, B.2    Novo, J.3
  • 5
    • 34250223731 scopus 로고
    • The finite element method for parabolic equations I. A posteriori error estimation
    • Bieterman M., and Babuška I. The finite element method for parabolic equations I. A posteriori error estimation. Numer. Math. 40 (1982) 339-371
    • (1982) Numer. Math. , vol.40 , pp. 339-371
    • Bieterman, M.1    Babuška, I.2
  • 6
    • 34250235371 scopus 로고
    • The finite element method for parabolic equations II. A posteriori error estimation and adaptive approach
    • Bieterman M., and Babuška I. The finite element method for parabolic equations II. A posteriori error estimation and adaptive approach. Numer. Math. 40 (1982) 373-406
    • (1982) Numer. Math. , vol.40 , pp. 373-406
    • Bieterman, M.1    Babuška, I.2
  • 7
    • 38249043795 scopus 로고
    • An adaptive method of lines with error control for parabolic equations of the reaction-diffusion type
    • Bieterman M., and Babuška I. An adaptive method of lines with error control for parabolic equations of the reaction-diffusion type. J. Comput. Phys. 63 (1986) 33-66
    • (1986) J. Comput. Phys. , vol.63 , pp. 33-66
    • Bieterman, M.1    Babuška, I.2
  • 8
    • 0035827103 scopus 로고    scopus 로고
    • A posteriori error estimation for the semidiscrete finite element method of parabolic differential equations
    • Babuška I., and Ohnimus S. A posteriori error estimation for the semidiscrete finite element method of parabolic differential equations. Comput. Methods Appl. Mech. Engrg. 190 (2001) 4691-4712
    • (2001) Comput. Methods Appl. Mech. Engrg. , vol.190 , pp. 4691-4712
    • Babuška, I.1    Ohnimus, S.2
  • 9
    • 0035630248 scopus 로고    scopus 로고
    • On one approach to a posteriori error estimates for evolution problems solved by the method of lines
    • Babuška I., Feistauer M., and Šolín P. On one approach to a posteriori error estimates for evolution problems solved by the method of lines. Numer. Math. 89 (2001) 225-256
    • (2001) Numer. Math. , vol.89 , pp. 225-256
    • Babuška, I.1    Feistauer, M.2    Šolín, P.3
  • 10
    • 21644485033 scopus 로고    scopus 로고
    • A posteriori analysis of the finite element discretization of some parabolic equations
    • Bergam A., Bernardi C., and Mghazli Z. A posteriori analysis of the finite element discretization of some parabolic equations. Math. Comput. 74 (2005) 1117-1138
    • (2005) Math. Comput. , vol.74 , pp. 1117-1138
    • Bergam, A.1    Bernardi, C.2    Mghazli, Z.3
  • 12
    • 0034190401 scopus 로고    scopus 로고
    • A postprocess based improvement of the spectral element method
    • de Frutos J., and Novo J. A postprocess based improvement of the spectral element method. Appl. Numer. Math. 33 (2000) 217-223
    • (2000) Appl. Numer. Math. , vol.33 , pp. 217-223
    • de Frutos, J.1    Novo, J.2
  • 13
    • 0034436855 scopus 로고    scopus 로고
    • A apectral element method for the Navier-Stokes equations with improved accuracy
    • de Frutos J., and Novo J. A apectral element method for the Navier-Stokes equations with improved accuracy. SIAM J. Numer. Anal. 38 (2000) 799-819
    • (2000) SIAM J. Numer. Anal. , vol.38 , pp. 799-819
    • de Frutos, J.1    Novo, J.2
  • 14
    • 0038042429 scopus 로고    scopus 로고
    • Postprocessing the linear finite element method
    • de Frutos J., and Novo J. Postprocessing the linear finite element method. SIAM. J. Numer. Anal. 40 (2002) 805-819
    • (2002) SIAM. J. Numer. Anal. , vol.40 , pp. 805-819
    • de Frutos, J.1    Novo, J.2
  • 15
    • 0037184250 scopus 로고    scopus 로고
    • A posteriori error estimation with the p version of the finite element method for nonlinear parabolic differential equations
    • de Frutos J., and Novo J. A posteriori error estimation with the p version of the finite element method for nonlinear parabolic differential equations. Comput. Methods Appl. Mech. Engrg. 191 (2002) 4893-4904
    • (2002) Comput. Methods Appl. Mech. Engrg. , vol.191 , pp. 4893-4904
    • de Frutos, J.1    Novo, J.2
  • 16
    • 21344439543 scopus 로고    scopus 로고
    • Element-wise a posteriori estimates based on hierarchical bases for nonlinear parabolic problems
    • de Frutos J., and Novo J. Element-wise a posteriori estimates based on hierarchical bases for nonlinear parabolic problems. Int. J. Numer. Methods Engrg. 63 (2005) 1146-1173
    • (2005) Int. J. Numer. Methods Engrg. , vol.63 , pp. 1146-1173
    • de Frutos, J.1    Novo, J.2
  • 17
    • 0001324638 scopus 로고    scopus 로고
    • Postprocessing the Galerkin method: a novel approach to approximate inertial manifolds
    • García-Archilla B., Novo J., and Titi E.S. Postprocessing the Galerkin method: a novel approach to approximate inertial manifolds. SIAM J. Numer. Anal. 35 (1998) 941-972
    • (1998) SIAM J. Numer. Anal. , vol.35 , pp. 941-972
    • García-Archilla, B.1    Novo, J.2    Titi, E.S.3
  • 18
    • 0038855060 scopus 로고    scopus 로고
    • An approximate inertial manifold approach to postprocessing Galerkin methods for the Navier-Stokes equations
    • García-Archilla B., Novo J., and Titi E.S. An approximate inertial manifold approach to postprocessing Galerkin methods for the Navier-Stokes equations. Math. Comput. 68 (1999) 893-911
    • (1999) Math. Comput. , vol.68 , pp. 893-911
    • García-Archilla, B.1    Novo, J.2    Titi, E.S.3
  • 19
    • 0000051734 scopus 로고    scopus 로고
    • Postprocessing the Galerkin method: the finite element case
    • García-Archilla B., and Titi E.S. Postprocessing the Galerkin method: the finite element case. SIAM. J. Numer. Anal. 37 (2000) 470-499
    • (2000) SIAM. J. Numer. Anal. , vol.37 , pp. 470-499
    • García-Archilla, B.1    Titi, E.S.2
  • 20
    • 0000966077 scopus 로고
    • Finite-element approximation of the nonstationary Navier-Stokes problem. Part I: Regularity of solutions and second-order error estimates for spatial discretization
    • Heywood J.G., and Rannacher R. Finite-element approximation of the nonstationary Navier-Stokes problem. Part I: Regularity of solutions and second-order error estimates for spatial discretization. SIAM J. Numer. Anal. 19 (1982) 275-311
    • (1982) SIAM J. Numer. Anal. , vol.19 , pp. 275-311
    • Heywood, J.G.1    Rannacher, R.2
  • 21
    • 0025416424 scopus 로고
    • Finite-element approximation of the nonstationary Navier-Stokes Problem. Part IV: Error analysis of second order time discretization
    • Heywood J.G., and Rannacher R. Finite-element approximation of the nonstationary Navier-Stokes Problem. Part IV: Error analysis of second order time discretization. SIAM J. Numer. Anal. 37 (1990) 353-384
    • (1990) SIAM J. Numer. Anal. , vol.37 , pp. 353-384
    • Heywood, J.G.1    Rannacher, R.2
  • 22
    • 33750850308 scopus 로고    scopus 로고
    • Elliptic reconstruction and a posteriori error estimates for fully discrete linear parabolic problems
    • Lakkis O., and Makridakis C. Elliptic reconstruction and a posteriori error estimates for fully discrete linear parabolic problems. Math. Comput. 75 (2006) 1627-1658
    • (2006) Math. Comput. , vol.75 , pp. 1627-1658
    • Lakkis, O.1    Makridakis, C.2
  • 23
    • 0030288775 scopus 로고    scopus 로고
    • Runge-Kutta time discretization of reaction-diffusion and Navier-Stokes equations: nonsmooth-data error estimates and applications to long-time behaviour
    • Lubich C., and Ostermann A. Runge-Kutta time discretization of reaction-diffusion and Navier-Stokes equations: nonsmooth-data error estimates and applications to long-time behaviour. Appl. Numer. Math. 22 (1996) 279-292
    • (1996) Appl. Numer. Math. , vol.22 , pp. 279-292
    • Lubich, C.1    Ostermann, A.2
  • 24
    • 1342297216 scopus 로고    scopus 로고
    • Elliptic reconstruction and a posteriori error estimates for parabolic problems
    • Makridakis C., and Nochetto R.H. Elliptic reconstruction and a posteriori error estimates for parabolic problems. SIAM J. Numer. Anal. 41 (2003) 1585-1594
    • (2003) SIAM J. Numer. Anal. , vol.41 , pp. 1585-1594
    • Makridakis, C.1    Nochetto, R.H.2
  • 25
    • 0028374973 scopus 로고
    • A posteriori error estimation with finite element semi and fully discrete methods for nonlinear parabolic equations in one space dimension
    • Moore P. A posteriori error estimation with finite element semi and fully discrete methods for nonlinear parabolic equations in one space dimension. SIAM J. Numer. Anal. 31 (1994) 149-169
    • (1994) SIAM J. Numer. Anal. , vol.31 , pp. 149-169
    • Moore, P.1
  • 26
    • 0242500938 scopus 로고    scopus 로고
    • Guaranteed a posteriori error estimation for fully discrete solutions of parabolic problems
    • Strouboulis T., Babuska I., and Datta D.K. Guaranteed a posteriori error estimation for fully discrete solutions of parabolic problems. Int. J. Numer. Methods Engrg. 56 (2003) 1243-1259
    • (2003) Int. J. Numer. Methods Engrg. , vol.56 , pp. 1243-1259
    • Strouboulis, T.1    Babuska, I.2    Datta, D.K.3
  • 28
    • 34250324786 scopus 로고    scopus 로고
    • Postprocessing the finite element method for semilinear parabolic problems
    • Yan Y. Postprocessing the finite element method for semilinear parabolic problems. SIAM J. Numer. Anal. 44 (2006) 1681-1702
    • (2006) SIAM J. Numer. Anal. , vol.44 , pp. 1681-1702
    • Yan, Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.