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Volumn 27, Issue 5, 2011, Pages 1340-1363

Analysis of some finite difference schemes for two-dimensional Ginzburg-Landau equation

Author keywords

2D Ginzburg Landau equation; convergence; finite difference method; solvability

Indexed keywords

CONVERGENCE; FINITE DIFFERENCE SCHEME; GINZBURG-LANDAU EQUATIONS; ITERATIVE ALGORITHM; NUMERICAL EXAMPLE; NUMERICAL SOLUTION; RATE OF CONVERGENCE; SECOND ORDER CONVERGENCE; SOLVABILITY; UNIFORM NORM;

EID: 79960820600     PISSN: 0749159X     EISSN: 10982426     Source Type: Journal    
DOI: 10.1002/num.20588     Document Type: Article
Times cited : (64)

References (48)
  • 1
    • 0000153785 scopus 로고    scopus 로고
    • Low dimensional behavior in the complex Ginzburg-Landau equation
    • C. Doering, J. D. Gibbon, D. Holm, and, B. Nicolaenko, Low dimensional behavior in the complex Ginzburg-Landau equation, Nonlinearity 1 (1998), 279-309.
    • (1998) Nonlinearity , vol.1 , pp. 279-309
    • Doering, C.1    Gibbon, J.D.2    Holm, D.3    Nicolaenko, B.4
  • 2
    • 0000322045 scopus 로고
    • Dimension of the attractor associated to the Ginzburg-Landau equation
    • J. M. Gnidaglia, and, B. Heron, Dimension of the attractor associated to the Ginzburg-Landau equation, Phy D 28 (1987), 282-304.
    • (1987) Phy D , vol.28 , pp. 282-304
    • Gnidaglia, J.M.1    Heron, B.2
  • 3
    • 0000781993 scopus 로고    scopus 로고
    • The complex Ginzburg-Landau equation as a model problem
    • C. D. Levemore, and, M. Oliver, The complex Ginzburg-Landau equation as a model problem, Lect Appl Math 31 (1996), 141-190.
    • (1996) Lect Appl Math , vol.31 , pp. 141-190
    • Levemore, C.D.1    Oliver, M.2
  • 4
    • 4244140192 scopus 로고
    • Induced trajectories and approximate interial manifolds for the Ginzburg-Landau partial differential equation
    • K. Promislow, Induced trajectories and approximate interial manifolds for the Ginzburg-Landau partial differential equation, Phy D 41 (1990), 232-252.
    • (1990) Phy D , vol.41 , pp. 232-252
    • Promislow, K.1
  • 5
    • 0000488017 scopus 로고
    • On the Cauchy problem for the 1 + 2 complex Ginzburg-Landau equation
    • C. Bu, On the Cauchy problem for the 1 + 2 complex Ginzburg-Landau equation, J Aust Math Soc ser B 36 (1994), 313-324.
    • (1994) J Aust Math Soc ser B , vol.36 , pp. 313-324
    • Bu, C.1
  • 6
    • 58149209984 scopus 로고
    • Finite dimensional behavior for the derivative Ginzburg-Landau equation in two spatial dimensions
    • B. Guo, and, B. Wang, Finite dimensional behavior for the derivative Ginzburg-Landau equation in two spatial dimensions, Phy D 89 (1995), 83-99.
    • (1995) Phy D , vol.89 , pp. 83-99
    • Guo, B.1    Wang, B.2
  • 7
    • 0034664295 scopus 로고    scopus 로고
    • Global existence of solutions to the deritivative Ginzburg-Landau equation
    • Y. Li, and, B. Guo, Global existence of solutions to the deritivative Ginzburg-Landau equation, J Math Anal Appl 249 (2000), 412-432.
    • (2000) J Math Anal Appl , vol.249 , pp. 412-432
    • Li, Y.1    Guo, B.2
  • 8
    • 0031365884 scopus 로고    scopus 로고
    • On the initial-value problem for the generalized two-dimensional Ginzburg-Landau equation
    • DOI 10.1006/jmaa.1997.5682, PII S0022247X97956821
    • H. Gao, and, J. Duan, On the initial value problem for the generized 2D Ginzburg-Landau equation, J Math Anal Appl 216 (1997), 536-548. (Pubitemid 127170529)
    • (1997) Journal of Mathematical Analysis and Applications , vol.216 , Issue.2 , pp. 536-548
    • Gao, H.1    Duan, J.2
  • 9
    • 0034216359 scopus 로고    scopus 로고
    • Asymptotics for the generized two dimensional Ginzburg-Landau equation
    • H. Gao, and, J. Duan, Asymptotics for the generized two dimensional Ginzburg-Landau equation, J Math Anal Appl 247 (2000), 198-216.
    • (2000) J Math Anal Appl , vol.247 , pp. 198-216
    • Gao, H.1    Duan, J.2
  • 10
    • 34547502301 scopus 로고    scopus 로고
    • Exponential attractor for the 3D Ginzburg-Landau type equation
    • DOI 10.1016/j.na.2006.10.005, PII S0362546X06006249
    • S. Lü, and, Q. Lu, Exponential attractor for the 3D Ginzburg-Landau type equation, Nonlinear Analysis 67 (2007), 3116-3135. (Pubitemid 47187941)
    • (2007) Nonlinear Analysis, Theory, Methods and Applications , vol.67 , Issue.11 , pp. 3116-3135
    • Lu, S.1    Lu, Q.2
  • 11
    • 33845704952 scopus 로고    scopus 로고
    • The dynamical behavior of the Ginzburg-Landau equation and its Fourier spectral approxmiation
    • S. Lü, The dynamical behavior of the Ginzburg-Landau equation and its Fourier spectral approxmiation, Numer Math 22 (2000), 1-9.
    • (2000) Numer Math , vol.22 , pp. 1-9
    • Lü, S.1
  • 12
    • 33748418943 scopus 로고    scopus 로고
    • Fourier spectral approximation to long-time behaviour of the derivative three-dimensional Ginzburg-Landau equation
    • DOI 10.1016/j.cam.2005.11.028, PII S0377042705007326
    • S. Lü, Q. Lu, and, E. H. Twizell, Fourier spectral approxmiation to long-time behavior of the derivative three-demensional Ginzburg-Landau equation, J Comput Appl Math 198 (2007), 167-186. (Pubitemid 44345060)
    • (2007) Journal of Computational and Applied Mathematics , vol.198 , Issue.1 , pp. 167-186
    • Lu, S.1    Lu, Q.2    Twizell, E.H.3
  • 13
    • 0039859605 scopus 로고
    • On the convergence of difference schemes for the Kuramoto-Tsuzuki equation and for systems of reaction-diffusion type
    • G. Z. Tsertsvadze, On the convergence of difference schemes for the Kuramoto-Tsuzuki equation and for systems of reaction-diffusion type, Zh Vychisl Math Math Fiz 31 (1991), 698-707.
    • (1991) Zh Vychisl Math Math Fiz , vol.31 , pp. 698-707
    • Tsertsvadze, G.Z.1
  • 14
    • 0040709337 scopus 로고    scopus 로고
    • On Tsertsvadze's difference scheme for the Kuramoto-Tsuzuki equation
    • Z. Z. Sun, On Tsertsvadze's difference scheme for the Kuramoto-Tsuzuki equation, J Comput Appl Math 98 (1998), 289-304.
    • (1998) J Comput Appl Math , vol.98 , pp. 289-304
    • Sun, Z.Z.1
  • 15
    • 0039859606 scopus 로고    scopus 로고
    • A linearized difference scheme for the kuramoto-tsuzuki equation
    • Z. Z. Sun, A linear difference scheme for the Kuramoto-Tsuzuki equation, J Comput Math 14 (1996), 1-7. (Pubitemid 126763853)
    • (1996) Journal of Computational Mathematics , vol.14 , Issue.1 , pp. 1-7
    • Sun, Z.Z.1
  • 16
    • 0041046545 scopus 로고    scopus 로고
    • A generalized Box scheme for the Kuramoto-Tsuzuki equation
    • Z. Z. Sun, A generalized Box scheme for the Kuramoto-Tsuzuki equation, J Southeast Univ 26 (1996), 87-92.
    • (1996) J Southeast Univ , vol.26 , pp. 87-92
    • Sun, Z.Z.1
  • 17
    • 0039267947 scopus 로고    scopus 로고
    • ∞ convergence of a linearized difference scheme for the Kuramoto-Tsuzuki equation
    • ∞ convergence of a linearized difference scheme for the Kuramoto-Tsuzuki equation, Nanjin Univer J Math Biquart 14 (1997), 5-9.
    • (1997) Nanjin Univer J Math Biquart , vol.14 , pp. 5-9
    • Sun, Z.Z.1
  • 19
    • 79952967244 scopus 로고    scopus 로고
    • Difference methods for computing the Ginzburg-Landau equation in two dimensions
    • 2009 November 6 [Epub ahead of print (DOI: 10.1002/num.20535)].
    • Q. Xu, and, Q. Chang, Difference methods for computing the Ginzburg-Landau equation in two dimensions, Numer Methods Partial Differential Eq 2009 November 6 [Epub ahead of print (DOI: 10.1002/num.20535)].
    • Numer Methods Partial Differential Eq
    • Xu, Q.1    Chang, Q.2
  • 20
    • 70349732515 scopus 로고
    • Implicit difference schemes for the generalized non-linear Schrödinger system, the convergence of numerical method for nonlinear Schrödinger equations
    • Y. Zhu, Implicit difference schemes for the generalized non-linear Schrödinger system, The convergence of numerical method for nonlinear Schrödinger equations, J Comput Math 1:2 (1983), 116-129.
    • (1983) J Comput Math , vol.12 , pp. 116-129
    • Zhu, Y.1
  • 21
    • 21844485652 scopus 로고
    • A second-order accurate linearized difference scheme for the two-dimensional Cahn-Hilliard equation
    • Z. Z. Sun, A second-order accurate linearized difference scheme for the two-dimensional Cahn-Hilliard equation, Math Comput 64 (1995), 1463-1471.
    • (1995) Math Comput , vol.64 , pp. 1463-1471
    • Sun, Z.Z.1
  • 22
    • 2442538708 scopus 로고
    • The convergence of numerical method for nonlinear Schrödinger equations
    • B. Guo, The convergence of numerical method for nonlinear Schrödinger equations, J Comput Math 4 (1986), 121-130.
    • (1986) J Comput Math , vol.4 , pp. 121-130
    • Guo, B.1
  • 23
    • 0031509850 scopus 로고    scopus 로고
    • Mixed finite element methods for a dynamical Ginzburg-Landau model in superconductivity
    • Z. Chen, Mixed finite element methods for a dynamical Ginzburg-Landau model in super-conductivity, Numer Math 76 (1997), 323-353. (Pubitemid 127367845)
    • (1997) Numerische Mathematik , vol.76 , Issue.3 , pp. 323-353
    • Chen, Z.1
  • 25
    • 0040770644 scopus 로고
    • Numerical studies of a non-stationary Ginzburg-Landau model for superconductivity
    • Z. Chen, and, K.-H. Hoffmann, Numerical studies of a non-stationary Ginzburg-Landau model for superconductivity, Adv Math Sci Appl 5 (1995), 363-389.
    • (1995) Adv Math Sci Appl , vol.5 , pp. 363-389
    • Chen, Z.1    Hoffmann, K.-H.2
  • 27
    • 84988159333 scopus 로고
    • On a non-stationary Ginzburg-Landau superconductivity model
    • Z. Chen, K.-H. Hoffmann, and, J. Liang, On a non-stationary Ginzburg-Landau superconductivity model, Math Meth Appl Sci 16 (1993), 855-875.
    • (1993) Math Meth Appl Sci , vol.16 , pp. 855-875
    • Chen, Z.1    Hoffmann, K.-H.2    Liang, J.3
  • 28
    • 0031173541 scopus 로고    scopus 로고
    • A linearized Crank-Nicolson-Galerkin method for the Ginzburg-Landau model
    • PII S1064827595283756
    • M. Mu, A linearized Crank-Nicolson-Galerkin method for the Ginzburg-Landau model, SIAM J Sci Comput 18 (1997), 1028-1039. (Pubitemid 127651304)
    • (1997) SIAM Journal of Scientific Computing , vol.18 , Issue.4 , pp. 1028-1039
    • Mu, M.1
  • 29
    • 0042410889 scopus 로고    scopus 로고
    • Adaptive galerkin methods with error control for a dynamical Ginzburg-Landau model in superconductivity
    • DOI 10.1137/S0036142998349102, PII S0036142998349102
    • Z. Chen, and, S. Dai, Adaptive Galerkin method with error control for a dynamical Ginzburg-Landau model in superconductivity, SIAM J Numer Anal 38 (2001), 1961-1985. (Pubitemid 33629641)
    • (2001) SIAM Journal on Numerical Analysis , vol.38 , Issue.6 , pp. 1961-1985
    • Chen, Z.1    Dai, S.2
  • 30
    • 0026838281 scopus 로고
    • Analysis and approximations of Ginzburg-Landau models for superconductivity
    • Q. Du, M. D. Gunzburger, and, J. S. Peterson, Analysis and approximations of Ginzburg-Landau models for superconductivity, SIAM Rev 34 (1992), 54-81.
    • (1992) SIAM Rev , vol.34 , pp. 54-81
    • Du, Q.1    Gunzburger, M.D.2    Peterson, J.S.3
  • 31
    • 0027608992 scopus 로고
    • Modeling and analysis of a periodic Ginzburg-Landau model for type-II superconductors
    • Q. Du, M. D. Gunzburger, and, J. S. Peterson, Modelling and analysis of a periodic Ginzburg-Landau model for type-II superconductors, SIAM J Appl Math 53 (1993), 689-717. (Pubitemid 23680322)
    • (1993) SIAM Journal on Applied Mathematics , vol.53 , Issue.3 , pp. 689-717
    • Du Qiang1    Gunzburger Max, D.2    Peterson Janet, S.3
  • 32
    • 21144474229 scopus 로고
    • Finite element approximation of superconductivity of a periodic Ginzburg-Landau model for type-II superconductors
    • Q. Du, M. D. Gunzburger, and, J. S. Peterson, Finite element approximation of superconductivity of a periodic Ginzburg-Landau model for type-II superconductors, Numer Math 64 (1993), 85-114.
    • (1993) Numer Math , vol.64 , pp. 85-114
    • Du, Q.1    Gunzburger, M.D.2    Peterson, J.S.3
  • 33
    • 84947888974 scopus 로고
    • Global existence and uniqueness of solutions of the time-dependent Ginzburg-Landau models for superconductivity
    • Q. Du, Global existence and uniqueness of solutions of the time-dependent Ginzburg-Landau models for superconductivity, Appl Anal 53 (1994), 1-17.
    • (1994) Appl Anal , vol.53 , pp. 1-17
    • Du, Q.1
  • 34
    • 38149146246 scopus 로고
    • Finite element methods for the time-dependent Ginzburg-Landau model of super-conductivity
    • Q. Du, Finite element methods for the time-dependent Ginzburg-Landau model of super-conductivity, Comp Math Appl 27 (1994), 119-133.
    • (1994) Comp Math Appl , vol.27 , pp. 119-133
    • Du, Q.1
  • 35
    • 0012941817 scopus 로고    scopus 로고
    • Computational methods for the time-dependent Ginzburg-Landau model of super-conductivity
    • editors, Science Press, New York
    • Q. Du, Computational methods for the time-dependent Ginzburg-Landau model of super-conductivity, Numerical methods for applied sciences, W. Cai, C. Shi, C. Shu, and, J. Xu, editors, Science Press, New York, 1996, pp. 51-65.
    • (1996) Numerical Methods for Applied Sciences , pp. 51-65
    • Du, Q.1    Cai, W.2    Shi, C.3    Shu, C.4    Xu, J.5
  • 36
    • 0009898683 scopus 로고    scopus 로고
    • Analysis and convergence of a covolume approximation of the ginzburg-landau model of superconductivity
    • Q. Du, R. Nicolaides, and, X. Wu, Analysis and convergence of a covolume approximation of the Ginzburg-Landau models of superconductivity, SIAM J Numer Anal 35 (1998), 1049-1072. (Pubitemid 128466396)
    • (1998) SIAM Journal on Numerical Analysis , vol.35 , Issue.3 , pp. 1049-1072
    • Du, Q.1    Nicolaides, R.A.2    Wu, X.3
  • 37
    • 0042100528 scopus 로고    scopus 로고
    • Constrained centroidal Voronoi tessellations on general surfaces
    • Q. Du, M. Gunzburger, and, L. Ju, Constrained centroidal Voronoi tessellations on general surfaces, SIAM J Sci Comput 24 (2003), 1488-1506.
    • (2003) SIAM J Sci Comput , vol.24 , pp. 1488-1506
    • Du, Q.1    Gunzburger, M.2    Ju, L.3
  • 38
    • 0042424790 scopus 로고    scopus 로고
    • Voronoi-based finite volume methods, optimal Voronoi meshes, and PDEs on the sphere
    • DOI 10.1016/S0045-7825(03)00394-3
    • Q. Du, M. Gunzburger, and, L. Ju, Voronoi-based finite volume methods, optimal Voronoi meshes, and PDEs on the sphere, Comput Meth Appl Mech Engrg 192 (2003), 3933-3957. (Pubitemid 37042315)
    • (2003) Computer Methods in Applied Mechanics and Engineering , vol.192 , Issue.35-36 , pp. 3933-3957
    • Du, Q.1    Gunzburger, M.D.2    Ju, L.3
  • 39
    • 26444609999 scopus 로고    scopus 로고
    • Diverse vortex dynamics in superfluids, current trends in scientific computing
    • Q. Du, Diverse vortex dynamics in superfluids, current trends in scientific computing, Contemp Math 329 (2003), 105-117.
    • (2003) Contemp Math , vol.329 , pp. 105-117
    • Du, Q.1
  • 40
    • 8744311511 scopus 로고    scopus 로고
    • Numerical simulations of the quantized vortices on a thin superconducting hollow sphere
    • DOI 10.1016/j.jcp.2004.06.009, PII S0021999104002402
    • Q. Du, and, L. Ju, Numerical simulations of the quantized vortices on a thin superconducting hollow sphere, J Comput Phys 201 (2004), 511-530. (Pubitemid 39525417)
    • (2004) Journal of Computational Physics , vol.201 , Issue.2 , pp. 511-530
    • Du, Q.1    Ju, L.2
  • 41
    • 0000209008 scopus 로고    scopus 로고
    • An alternating Crank-Nicolson method for decoupling the Ginzburg-Landau equations
    • M. Mu, and, Y. Huang, A alternating Crank-Nicolson method for decoupling the Ginzburg-Landau equations, SIAM J Numer Anal 35 (1998), 1740-1761. (Pubitemid 128464140)
    • (1998) SIAM Journal on Numerical Analysis , vol.35 , Issue.5 , pp. 1740-1761
    • Mu, M.1    Huang, Y.2
  • 42
    • 0038992234 scopus 로고
    • Computer simulation of a two-dimensional type-II superconductor in a magnetic field
    • Y. Enomoto, and, R. Kato, Computer simulation of a two-dimensional type-II superconductor in a magnetic field, J Phys Condens Matter 3 (1991), 375-380.
    • (1991) J Phys Condens Matter , vol.3 , pp. 375-380
    • Enomoto, Y.1    Kato, R.2
  • 44
    • 0037054261 scopus 로고    scopus 로고
    • A fast semi-implicit finite difference method for the TDGL equation
    • T. Winiecki, and, C. S. Adams, A fast semi-implicit finite difference method for the TDGL equation, J comput phys 179 (2002), 127-139.
    • (2002) J Comput Phys , vol.179 , pp. 127-139
    • Winiecki, T.1    Adams, C.S.2
  • 45
    • 0000671882 scopus 로고    scopus 로고
    • Simulating vortex motion in superconducting films with the time-dependent Ginzburg-Landau equations
    • E. Coskun, and, M. K. Kwong, Simulating vortex motion in superconducting films with the time-dependent Ginzburg-Landau equations, Nonlinearity 10 (1997), 579.
    • (1997) Nonlinearity , vol.10 , pp. 579
    • Coskun, E.1    Kwong, M.K.2
  • 46
    • 0034256719 scopus 로고    scopus 로고
    • The force-free case in three-dimensional superconductors: A computational study
    • J. F. Blackburn, A. Campbell, and, E. K. H. Salje, The force-free case in three-dimensional superconductors: a computational study, Philos Mag B 80 (2000), 1455.
    • (2000) Philos Mag B , vol.80 , pp. 1455
    • Blackburn, J.F.1    Campbell, A.2    Salje, E.K.H.3


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