메뉴 건너뛰기




Volumn 180, Issue 2, 2006, Pages 614-621

The convergence of fully discrete Galerkin approximations for the Benjamin-Bona-Mahony (BBM) equation

Author keywords

BBM equation; Conservation of energy; Crank Nicolson scheme; Error estimates; Existence; Extrapolation; Finite element method; Uniqueness

Indexed keywords

APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; ENERGY CONSERVATION; ERROR ANALYSIS; EXTRAPOLATION; FINITE ELEMENT METHOD; NONLINEAR EQUATIONS;

EID: 33748977285     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2005.12.046     Document Type: Article
Times cited : (81)

References (17)
  • 1
    • 33748953746 scopus 로고
    • Superconvergence of finite element approximation to the solution of a Sobolev equation in a single space variable
    • Arnold D.N., Douglas Jr. J., and Thomée V. Superconvergence of finite element approximation to the solution of a Sobolev equation in a single space variable. Math. Comput. 27 (1981) 737-743
    • (1981) Math. Comput. , vol.27 , pp. 737-743
    • Arnold, D.N.1    Douglas Jr., J.2    Thomée, V.3
  • 3
    • 0001119719 scopus 로고
    • The initial-value problem for the Korteweg-de Vries equation
    • Bona J.L., and Smith R. The initial-value problem for the Korteweg-de Vries equation. Philos. Trans. Roy. Soc. London A 278 (1975) 555-601
    • (1975) Philos. Trans. Roy. Soc. London A , vol.278 , pp. 555-601
    • Bona, J.L.1    Smith, R.2
  • 4
    • 0040374231 scopus 로고
    • Existence and uniqueness theorems for solutions of nonlinear boundary value problems
    • Applications of Nonlinear Partial Differential Equations. Finn R. (Ed), Amer. Math. Soc., Providence
    • Browder F.E. Existence and uniqueness theorems for solutions of nonlinear boundary value problems. In: Finn R. (Ed). Applications of Nonlinear Partial Differential Equations. Proc. Symp. Appl. Math. 17 (1965), Amer. Math. Soc., Providence 24-49
    • (1965) Proc. Symp. Appl. Math. 17 , pp. 24-49
    • Browder, F.E.1
  • 6
    • 49549142812 scopus 로고
    • Numerical studies of the regularized long-wave equations I: numerical methods
    • Eilbeck J.C., and McGuire G.R. Numerical studies of the regularized long-wave equations I: numerical methods. J. Comput. Phys. 19 (1975) 43-57
    • (1975) J. Comput. Phys. , vol.19 , pp. 43-57
    • Eilbeck, J.C.1    McGuire, G.R.2
  • 7
    • 0011412428 scopus 로고
    • Time-stepping Galerkin methods for nonlinear Sobolev partial differential equation
    • Ewing R.E. Time-stepping Galerkin methods for nonlinear Sobolev partial differential equation. SIAM J. Numer. Anal. 15 (1978) 1125-1150
    • (1978) SIAM J. Numer. Anal. , vol.15 , pp. 1125-1150
    • Ewing, R.E.1
  • 8
    • 0040476053 scopus 로고
    • Weak solutions for a nonlinear dispersive equation
    • Medeiros L.A., and Milla Miranda M. Weak solutions for a nonlinear dispersive equation. J. Math. Anal. Appl. 59 (1977) 432-441
    • (1977) J. Math. Anal. Appl. , vol.59 , pp. 432-441
    • Medeiros, L.A.1    Milla Miranda, M.2
  • 9
    • 0040224978 scopus 로고
    • Existence and uniqueness for periodic solutions of the Benjamin-Bona-Mahony equation
    • Medeiros L.A., and Perla Menzela G. Existence and uniqueness for periodic solutions of the Benjamin-Bona-Mahony equation. SIAM J. Math. Anal. 8 (1977) 792-799
    • (1977) SIAM J. Math. Anal. , vol.8 , pp. 792-799
    • Medeiros, L.A.1    Perla Menzela, G.2
  • 10
    • 51249190726 scopus 로고
    • Weak solutions of a modified KdV equation
    • Milla Miranda M. Weak solutions of a modified KdV equation. Bol. Soc. Brasil. Mat. 6 (1975) 57-63
    • (1975) Bol. Soc. Brasil. Mat. , vol.6 , pp. 57-63
    • Milla Miranda, M.1
  • 12
    • 33748960264 scopus 로고    scopus 로고
    • On fully discrete Galerkin methods for the Cahn-Hilliard equation
    • Omrani K. On fully discrete Galerkin methods for the Cahn-Hilliard equation. Math. Model. Anal. 9 4 (2004) 313-326
    • (2004) Math. Model. Anal. , vol.9 , Issue.4 , pp. 313-326
    • Omrani, K.1
  • 13
    • 26444462611 scopus 로고    scopus 로고
    • Convergence of Galerkin approximations for the Kuramoto-Tsuzuki equation
    • Omrani K. Convergence of Galerkin approximations for the Kuramoto-Tsuzuki equation. Numer. Meth. Partial Diff. Eq. 21 5 (2005) 961-975
    • (2005) Numer. Meth. Partial Diff. Eq. , vol.21 , Issue.5 , pp. 961-975
    • Omrani, K.1
  • 14
    • 84958444374 scopus 로고
    • Calculations of the development of an undular bore
    • Peregrine D.H. Calculations of the development of an undular bore. J. Fluid Mech. 25 (1966) 321-330
    • (1966) J. Fluid Mech. , vol.25 , pp. 321-330
    • Peregrine, D.H.1
  • 15
    • 51249190381 scopus 로고
    • Galerkin methods applied to the Benjamin-Bona-Mahony equation
    • Raupp M.A. Galerkin methods applied to the Benjamin-Bona-Mahony equation. Bol. Soc. Brasil. Mat. 6 (1975) 65-77
    • (1975) Bol. Soc. Brasil. Mat. , vol.6 , pp. 65-77
    • Raupp, M.A.1
  • 16
    • 33748954843 scopus 로고
    • Springer-verlag, Berlin
    • Thomée V. Galerkin Finite Element Methods for Parabolic Problems. L.N.M vol. 1054 (1984), Springer-verlag, Berlin
    • (1984) L.N.M , vol.1054
    • Thomée, V.1
  • 17
    • 0041983388 scopus 로고
    • Error estimates for a Galerkin method for a class of model equations for long waves
    • Wahlbin L. Error estimates for a Galerkin method for a class of model equations for long waves. Numer. Math. 23 (1975) 289-303
    • (1975) Numer. Math. , vol.23 , pp. 289-303
    • Wahlbin, L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.