메뉴 건너뛰기




Volumn 36, Issue 6, 1999, Pages 1779-1807

A space-time finite element method for the nonlinear Schrödinger equation: The continuous Galerkin method

Author keywords

Continuous Galerkin method; Nonlinear Schr dinger equation

Indexed keywords


EID: 0043232734     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142997330111     Document Type: Article
Times cited : (113)

References (24)
  • 1
    • 0031485921 scopus 로고    scopus 로고
    • Solving the system of equations arising in the discretization of some nonlinear pde's by implicit Runge-Kutta methods
    • G. D. AKRIVIS, V. A. DOUGALIS, AND O. A. KARAKASHIAN, Solving the system of equations arising in the discretization of some nonlinear pde's by implicit Runge-Kutta methods, RAIRO Modél. Math. Anal. Numér., 31 (1997), pp. 251-288.
    • (1997) RAIRO Modél. Math. Anal. Numér. , vol.31 , pp. 251-288
    • Akrivis, G.D.1    Dougalis, V.A.2    Karakashian, O.A.3
  • 2
    • 84966201439 scopus 로고
    • Continuous finite elements in space and time for the heat equation
    • A. K. AZIZ AND P. MONK, Continuous finite elements in space and time for the heat equation, Math. Comp., 52 (1989), pp. 255-274.
    • (1989) Math. Comp. , vol.52 , pp. 255-274
    • Aziz, A.K.1    Monk, P.2
  • 3
    • 0029104726 scopus 로고
    • Conservative, high-order numerical schemes for the generalized Korteweg-de Vries equation
    • J. L. BONA, V. A. DOUGALIS, O. A. KARAKASHIAN, AND W. R. MCKINNEY, Conservative, high-order numerical schemes for the generalized Korteweg-de Vries equation, Phil. Trans. Roy. Soc. London A, 351 (1995), pp. 107-164.
    • (1995) Phil. Trans. Roy. Soc. London a , vol.351 , pp. 107-164
    • Bona, J.L.1    Dougalis, V.A.2    Karakashian, O.A.3    Mckinney, W.R.4
  • 4
    • 38149144812 scopus 로고
    • Continuous finite elements in space and time for the nonhomogeneous wave equation
    • L. BALES AND I. LASIECKA, Continuous finite elements in space and time for the nonhomogeneous wave equation, Comput. Math. Appl., 27 (1994), pp. 91-102.
    • (1994) Comput. Math. Appl. , vol.27 , pp. 91-102
    • Bales, L.1    Lasiecka, I.2
  • 6
    • 0040374231 scopus 로고
    • Existence and uniqueness theorems for solutions of nonlinear boundary value problems
    • R. Finn, ed., AMS, Providence, RI
    • F. E. BROWDER, Existence and uniqueness theorems for solutions of nonlinear boundary value problems, Applications of Partial Differential Equations, R. Finn, ed., AMS, Providence, RI, 1965, pp. 24-29.
    • (1965) Applications of Partial Differential Equations , pp. 24-29
    • Browder, F.E.1
  • 7
    • 84966243417 scopus 로고
    • 2-projection onto finite element spaces
    • 2-projection onto finite element spaces, Math. Comp., 48 (1987), pp. 521-532.
    • (1987) Math. Comp. , vol.48 , pp. 521-532
    • Crouzeix, M.1    Thomée, V.2
  • 10
    • 0039270375 scopus 로고    scopus 로고
    • A time- and space-adaptive algorithm for the linear time-dependent Schrödinger equation
    • W. DÖRFLER, A time- and space-adaptive algorithm for the linear time-dependent Schrödinger equation, Numer. Math., 73 (1996), pp. 419-448.
    • (1996) Numer. Math. , vol.73 , pp. 419-448
    • Dörfler, W.1
  • 11
    • 0002111330 scopus 로고
    • Mesh modification for evolution equations
    • T. DUPONT, Mesh modification for evolution equations, Math. Comp., 39 (1982), pp. 85-107.
    • (1982) Math. Comp. , vol.39 , pp. 85-107
    • Dupont, T.1
  • 12
    • 0026106415 scopus 로고
    • Adaptive finite element methods for parabolic problems I: A linear model problem
    • K. ERIKSSON AND C. JOHNSON, Adaptive finite element methods for parabolic problems I: A linear model problem, SIAM J. Numer. Anal., 28 (1991), pp. 43-77.
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 43-77
    • Eriksson, K.1    Johnson, C.2
  • 14
    • 84904150653 scopus 로고
    • Adaptive finite element methods for parabolic problems IV: Nonlinear problems
    • K. ERIKSSON AND C. JOHNSON, Adaptive finite element methods for parabolic problems IV: Nonlinear problems, SIAM J. Numer. Anal., 32 (1995), pp. 1729-1749.
    • (1995) SIAM J. Numer. Anal. , vol.32 , pp. 1729-1749
    • Eriksson, K.1    Johnson, C.2
  • 15
    • 0000139680 scopus 로고
    • Global error control for the continuous Galerkin finite element method for ordinary differential equations
    • D. ESTEP AND D. A. FRENCH, Global error control for the continuous Galerkin finite element method for ordinary differential equations, RAIRO Math. Modél. Numér. Anal., 28 (1994), pp. 815-852.
    • (1994) RAIRO Math. Modél. Numér. Anal. , vol.28 , pp. 815-852
    • Estep, D.1    French, D.A.2
  • 16
    • 0023329117 scopus 로고
    • Analysis of a continuous finite element method for hyperbolic equations
    • R. S. FALK AND G. R. RICHTER, Analysis of a continuous finite element method for hyperbolic equations, SIAM J. Numer. Anal., 24 (1986), pp. 257-278.
    • (1986) SIAM J. Numer. Anal. , vol.24 , pp. 257-278
    • Falk, R.S.1    Richter, G.R.2
  • 17
    • 0030376796 scopus 로고    scopus 로고
    • A continuous space-time finite element method for the wave equation
    • D. A. FRENCH AND T. E. PETERSON, A continuous space-time finite element method for the wave equation, Math. Comp., 65 (1996), pp. 491-506.
    • (1996) Math. Comp. , vol.65 , pp. 491-506
    • French, D.A.1    Peterson, T.E.2
  • 18
    • 84968508862 scopus 로고
    • One-step piecewise polynomial Galerkin methods for initial value problems
    • B. L. HULME, One-step piecewise polynomial Galerkin methods for initial value problems, Math. Comp., 26 (1972), pp. 415-426.
    • (1972) Math. Comp. , vol.26 , pp. 415-426
    • Hulme, B.L.1
  • 19
    • 0027578339 scopus 로고
    • On optimal order error estimates for the nonlinear Schrödinger equation
    • O. KARAKASHIAN, G. D. AKRIVIS, AND V. A. DOUGALIS, On optimal order error estimates for the nonlinear Schrödinger equation, SIAM J. Numer. Anal., 30 (1993), pp. 377-400.
    • (1993) SIAM J. Numer. Anal. , vol.30 , pp. 377-400
    • Karakashian, O.1    Akrivis, G.D.2    Dougalis, V.A.3
  • 22
    • 84968481060 scopus 로고
    • Interior maximum-norm estimates for finite element methods, Part II
    • A. H. SCHATZ AND L. B. WAHLBIN, Interior maximum-norm estimates for finite element methods, Part II, Math. Comp., 64 (1995), pp. 907-928.
    • (1995) Math. Comp. , vol.64 , pp. 907-928
    • Schatz, A.H.1    Wahlbin, L.B.2
  • 23
    • 0041764781 scopus 로고
    • The nonlinear Schrödinger equation
    • G. M. de la Penha and L. A. J. Medeiros, eds., North-Holland, Amsterdam
    • W. A. STRAUSS, The nonlinear Schrödinger equation, in Contemporary Developments in Continuum Mechanics and P.D.E.'s, G. M. de la Penha and L. A. J. Medeiros, eds., North-Holland, Amsterdam, 1978, pp. 452-465.
    • (1978) Contemporary Developments in Continuum Mechanics and P.D.E.'s , pp. 452-465
    • Strauss, W.A.1
  • 24
    • 0003208045 scopus 로고
    • Galerkin Finite Element Methods for Parabolic Problems
    • Springer-Verlag, Berlin
    • V. THOMÉE, Galerkin Finite Element Methods for Parabolic Problems, Lecture Notes in Math., 1054, Springer-Verlag, Berlin, 1984.
    • (1984) Lecture Notes in Math. , vol.1054
    • Thomée, V.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.