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Volumn 46, Issue 2, 2007, Pages 121-139

The impact of parameter selection on the performance of an automatic adaptive code for solving reaction-diffusion equations in three dimensions

Author keywords

Adaptive high order finite element methods; Method of lines

Indexed keywords


EID: 36448997044     PISSN: 10171398     EISSN: 15729265     Source Type: Journal    
DOI: 10.1007/s11075-007-9131-1     Document Type: Article
Times cited : (1)

References (37)
  • 1
    • 0033293882 scopus 로고    scopus 로고
    • A posteriori finite element error estimation for diffusion problems
    • Adjerid, S., Belguendouz, B., Flaherty, J.E.: A posteriori finite element error estimation for diffusion problems. SIAM J. Sci. Comput. 21, 728-746 (1999)
    • (1999) SIAM J. Sci. Comput. , vol.21 , pp. 728-746
    • Adjerid, S.1    Belguendouz, B.2    Flaherty, J.E.3
  • 2
    • 0032363607 scopus 로고    scopus 로고
    • Implicit-explicit multistep finite element methods for nonlinear parabolic problems
    • Akrivis, G., Crouzeix, M., Makridakis, C.: Implicit-explicit multistep finite element methods for nonlinear parabolic problems. Math. Comput. 67, 457-477 (1998)
    • (1998) Math. Comput. , vol.67 , pp. 457-477
    • Akrivis, G.1    Crouzeix, M.2    Makridakis, C.3
  • 3
    • 0001737039 scopus 로고
    • Implicit-explicit methods for time-dependent partial differential equations
    • Ascher, U.M., Ruuth, S.J., Wetton, B.T.R.: Implicit-explicit methods for time-dependent partial differential equations. SIAM J. Numer. Anal. 32, 797-823 (1995)
    • (1995) SIAM J. Numer. Anal. , vol.32 , pp. 797-823
    • Ascher, U.M.1    Ruuth, S.J.2    Wetton, B.T.R.3
  • 4
    • 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., Šolin, P.: On one approach to a posteriori error estimates for evolution problems solved by the method of lines. Numer. Math. 89, 225-256 (2001)
    • (2001) Numer. Math. , vol.89 , pp. 225-256
    • Babuška, I.1    Feistauer, M.2    Šolin, P.3
  • 5
    • 0035827103 scopus 로고    scopus 로고
    • A posteriori error estimation for the semidiscrete finite element of parabolic differential equations
    • Babuška, I., Ohnimus, S.: A posteriori error estimation for the semidiscrete finite element of parabolic differential equations. Comput. Methods Appl. Mech. Eng. 190, 4691-4712 (2001)
    • (2001) Comput. Methods Appl. Mech. Eng. , vol.190 , pp. 4691-4712
    • Babuška, I.1    Ohnimus, S.2
  • 8
    • 0000286812 scopus 로고
    • Using Krylov methods in the solution of large-scale differential- algebraic systems
    • Brown, P.N., Hindmarsh, A.C., Petzold, L.R.: Using Krylov methods in the solution of large-scale differential-algebraic systems. SIAM J. Sci. Comput. 15, 1467-1488 (1994)
    • (1994) SIAM J. Sci. Comput. , vol.15 , pp. 1467-1488
    • Brown, P.N.1    Hindmarsh, A.C.2    Petzold, L.R.3
  • 11
    • 0016443950 scopus 로고
    • Comparing numerical methods for stiff systems of ODEs
    • Enright, W.H., Hull, T.E., Lindberg, B.: Comparing numerical methods for stiff systems of ODEs. BIT 15, 10-48 (1975)
    • (1975) BIT , vol.15 , pp. 10-48
    • Enright, W.H.1    Hull, T.E.2    Lindberg, B.3
  • 12
    • 0000871598 scopus 로고
    • Integrated space-time adaptive hp-refinement methods for parabolic systems
    • Flaherty, J.E., Moore, P.K.: Integrated space-time adaptive hp-refinement methods for parabolic systems. Appl. Numer. Math. 16, 317-341 (1995)
    • (1995) Appl. Numer. Math. , vol.16 , pp. 317-341
    • Flaherty, J.E.1    Moore, P.K.2
  • 14
    • 21344439543 scopus 로고    scopus 로고
    • Element-wise a posteriori estimates based on hierarchical bases for non-linear parabolic problems
    • de Frutos, J., Novo, J.: Element-wise a posteriori estimates based on hierarchical bases for non-linear parabolic problems. Int. J. Numer. Methods Eng. 63, 1146-1173 (2005)
    • (2005) Int. J. Numer. Methods Eng. , vol.63 , pp. 1146-1173
    • De Frutos, J.1    Novo, J.2
  • 16
    • 0001811061 scopus 로고
    • ODEPACK, a systemized collection of ODE solvers
    • IMACS/North Holland Amsterdam
    • Hindmarsh, A.C.: ODEPACK, a systemized collection of ODE solvers. In: Stepleman, R.S., et al. (eds.) Scientific Computing, pp. 55-64. IMACS/North Holland, Amsterdam (1983)
    • (1983) Scientific Computing , pp. 55-64
    • Hindmarsh, A.C.1    Stepleman, R.S.2
  • 18
    • 0031643387 scopus 로고    scopus 로고
    • Adaptive FEM for reaction-diffusion equations
    • Lang, J.: Adaptive FEM for reaction-diffusion equations. Appl. Numer. Math. 26, 105-116 (1998)
    • (1998) Appl. Numer. Math. , vol.26 , pp. 105-116
    • Lang, J.1
  • 19
    • 0000309178 scopus 로고
    • Balancing space and time errors in the method of lines for parabolic equations
    • Lawson, J., Berzins, M., Dew, P.M.: Balancing space and time errors in the method of lines for parabolic equations. SIAM J. Sci. Statist. Comput. 12, 573-594 (1991)
    • (1991) SIAM J. Sci. Statist. Comput. , vol.12 , pp. 573-594
    • Lawson, J.1    Berzins, M.2    Dew, P.M.3
  • 20
    • 1342297216 scopus 로고    scopus 로고
    • Elliptic reconstruction and a posteriori error estimates for parabolic problems
    • Makridakis, C., Nochetto, R.H.: Elliptic reconstruction and a posteriori error estimates for parabolic problems. SIAM J. Numer. Anal. 41, 1585-1594 (2003)
    • (2003) SIAM J. Numer. Anal. , vol.41 , pp. 1585-1594
    • Makridakis, C.1    Nochetto, R.H.2
  • 21
    • 34248512617 scopus 로고    scopus 로고
    • Effects of basis selection and h-refinement on error estimator reliability and solution efficiency for higher-order methods in three space dimensions
    • Moore, P.K.: Effects of basis selection and h-refinement on error estimator reliability and solution efficiency for higher-order methods in three space dimensions. Int. J. Numer. Anal. Mod. 3, 21-51 (2006)
    • (2006) Int. J. Numer. Anal. Mod. , vol.3 , pp. 21-51
    • Moore, P.K.1
  • 22
    • 0141514387 scopus 로고    scopus 로고
    • Implicit interpolation error-based error estimation for reaction-diffusion equations in two space dimensions
    • Moore, P.K.: Implicit interpolation error-based error estimation for reaction-diffusion equations in two space dimensions. Comput. Methods Appl. Mech. Eng. 192, 4379-4401 (2003)
    • (2003) Comput. Methods Appl. Mech. Eng. , vol.192 , pp. 4379-4401
    • Moore, P.K.1
  • 23
    • 0038792196 scopus 로고    scopus 로고
    • An incomplete assembly with thresholding algorithm for systems of reaction-diffusion equations in three dimensions: IAT for reaction-diffusion systems
    • Moore, P.K.: An incomplete assembly with thresholding algorithm for systems of reaction-diffusion equations in three dimensions: IAT for reaction-diffusion systems. J. Comput. Phys. 189, 130-158 (2003)
    • (2003) J. Comput. Phys. , vol.189 , pp. 130-158
    • Moore, P.K.1
  • 24
    • 0141575485 scopus 로고    scopus 로고
    • Applications of Lobatto polynomials to an adaptive finite element method: A posteriori error estimates for hp-adaptivity and grid-to-grid interpolation
    • Moore, P.K.: Applications of Lobatto polynomials to an adaptive finite element method: a posteriori error estimates for hp-adaptivity and grid-to-grid interpolation. Numer. Math. 94, 367-401 (2003)
    • (2003) Numer. Math. , vol.94 , pp. 367-401
    • Moore, P.K.1
  • 25
    • 0033294920 scopus 로고    scopus 로고
    • An adaptive finite element method for parabolic differential systems: Some algorithmic considerations in solving in three space dimensions
    • Moore, P.K.: An adaptive finite element method for parabolic differential systems: some algorithmic considerations in solving in three space dimensions. SIAM J. Sci. Comput. 21, 1567-1586 (2000)
    • (2000) SIAM J. Sci. Comput. , vol.21 , pp. 1567-1586
    • Moore, P.K.1
  • 26
    • 0030081174 scopus 로고    scopus 로고
    • A comparison of preconditioners in the solution of parabolic systems in three space dimensions using DASPK and a higher order finite element method
    • Moore, P.K., Dillon, R.H.: A comparison of preconditioners in the solution of parabolic systems in three space dimensions using DASPK and a higher order finite element method. Appl. Numer. Math. 20, 117-128 (1996)
    • (1996) Appl. Numer. Math. , vol.20 , pp. 117-128
    • Moore, P.K.1    Dillon, R.H.2
  • 27
    • 0000646363 scopus 로고
    • Comparison of adaptive methods for one-dimensional parabolic systems
    • Moore, P.K.: Comparison of adaptive methods for one-dimensional parabolic systems. Appl. Numer. Math. 16, 471-488 (1995)
    • (1995) Appl. Numer. Math. , vol.16 , pp. 471-488
    • Moore, P.K.1
  • 28
    • 0001248878 scopus 로고
    • Implicit-explicit methods for reaction-diffusion problems in pattern formation
    • Ruuth, S.: Implicit-explicit methods for reaction-diffusion problems in pattern formation. J. Math. Biol. 34, 148-176 (1995)
    • (1995) J. Math. Biol. , vol.34 , pp. 148-176
    • Ruuth, S.1
  • 29
    • 84985408358 scopus 로고
    • ILUT: A dual threshold incomplete LU factorization
    • Saad, Y.: ILUT: a dual threshold incomplete LU factorization. Numer. Linear Algebra Appl. 1, 387-402 (1994)
    • (1994) Numer. Linear Algebra Appl. , vol.1 , pp. 387-402
    • Saad, Y.1
  • 30
    • 0000048673 scopus 로고
    • GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems
    • Saad, Y., Schultz, M.H.: GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 7, 856-869 (1986)
    • (1986) SIAM J. Sci. Stat. Comput. , vol.7 , pp. 856-869
    • Saad, Y.1    Schultz, M.H.2
  • 35
    • 2442718057 scopus 로고    scopus 로고
    • A high-order global spatially adaptive collocation method for 1-D parabolic PDEs
    • Wang, R., Keast, P., Muir, P.: A high-order global spatially adaptive collocation method for 1-D parabolic PDEs. Appl. Numer. Math. 50, 239-250 (2004)
    • (2004) Appl. Numer. Math. , vol.50 , pp. 239-250
    • Wang, R.1    Keast, P.2    Muir, P.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.