메뉴 건너뛰기




Volumn 21, Issue 4, 1999, Pages 1567-1586

An adaptive finite element method for parabolic differential systems: Some algorithmic considerations in solving in three space dimensions

Author keywords

Adaptive finite element methods; Irregular grids

Indexed keywords

ADAPTIVE FINITE ELEMENT METHOD; BACKWARD DIFFERENCE FORMULA CODE; IRREGULAR GRIDS; PARABOLIC DIFFERENTIAL SYSTEMS; SPACE DIMENSIONS;

EID: 0033294920     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827598349197     Document Type: Article
Times cited : (20)

References (23)
  • 1
    • 0033410127 scopus 로고    scopus 로고
    • A posteriori error estimation for the finite element method-of-lines solution of parabolic problems
    • S. ADJERID, J.E. FLAHERTY, AND I. BADUSKA, A posteriori error estimation for the finite element method-of-lines solution of parabolic problems, Math. Models Methods Appl. Sci., 9 (1999), pp. 261-286.
    • (1999) Math. Models Methods Appl. Sci. , vol.9 , pp. 261-286
    • Adjerid, S.1    Flaherty, J.E.2    Baduska, I.3
  • 2
  • 3
    • 0000613724 scopus 로고
    • Error estimates for adaptive finite element computations
    • I. BABUSKA AND W.C. RHEINBOLDT, Error estimates for adaptive finite element computations, SIAM J. Numer. Anal., 15 (1978), pp. 736-754.
    • (1978) SIAM J. Numer. Anal. , vol.15 , pp. 736-754
    • Babuska, I.1    Rheinboldt, W.C.2
  • 4
    • 0004806316 scopus 로고
    • Reliable error estimation and mesh adaptation for the finite element method
    • North-Holland, New York
    • I. BABUSKA AND W.C. RHEINBOLDT, Reliable error estimation and mesh adaptation for the finite element method, in Computational Methods in Nonlinear Mechanics, North-Holland, New York, 1980, pp. 67-108.
    • (1980) Computational Methods in Nonlinear Mechanics , pp. 67-108
    • Babuska, I.1    Rheinboldt, W.C.2
  • 5
    • 0002564037 scopus 로고
    • The efficient implementation of local mesh refinement algorithms
    • I. Babuska, J. Chandra, and J.E. Flaherty, eds., SIAM, Philadelphia
    • R.E. BANK, The efficient implementation of local mesh refinement algorithms, in Adaptive Computational Methods for Partial Differential Equations, I. Babuska, J. Chandra, and J.E. Flaherty, eds., SIAM, Philadelphia, 1983, pp. 74-81.
    • (1983) Adaptive Computational Methods for Partial Differential Equations , pp. 74-81
    • Bank, R.E.1
  • 7
    • 0000286812 scopus 로고
    • Using Krylov methods in the solution of large-scale differential-algebraic systems
    • P.N. BROWN, A.C. HINDMARSH, AND L.R. PETZOLD, Using Krylov methods in the solution of large-scale differential-algebraic systems, SIAM J. Sci. Comput., 15 (1994), pp. 1467-1488.
    • (1994) SIAM J. Sci. Comput. , vol.15 , pp. 1467-1488
    • Brown, P.N.1    Hindmarsh, A.C.2    Petzold, L.R.3
  • 8
    • 0032008348 scopus 로고    scopus 로고
    • Edge of chaos and local activity domain of Fitzhugh-Nagumo equation
    • R. DOGARU AND L.O. CHUA, Edge of chaos and local activity domain of Fitzhugh-Nagumo equation, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8 (1998), pp. 211-257.
    • (1998) Internat. J. Bifur. Chaos Appl. Sci. Engrg. , vol.8 , pp. 211-257
    • Dogaru, R.1    Chua, L.O.2
  • 9
    • 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
  • 10
    • 0003983881 scopus 로고
    • J.E. FLAHERTY, P.J. PASLOW, M.S. SHEPHARD, AND J.D. VASILAKIS, EDS., SIAM, Philadelphia, PA
    • J.E. FLAHERTY, P.J. PASLOW, M.S. SHEPHARD, AND J.D. VASILAKIS, EDS., Adaptive Methods for Partial Differential Equations, SIAM, Philadelphia, PA, 1989.
    • (1989) Adaptive Methods for Partial Differential Equations
  • 11
    • 0002176065 scopus 로고
    • Experiments with an adaptive h-, p-, and r-refinement finite element method for parabolic systems
    • G.D. Byrne and W.E. Schiesser, eds., World Scientific, Singapore
    • J.E. FLAHERTY AND Y. WANG, Experiments with an adaptive h-, p-, and r-refinement finite element method for parabolic systems, in Recent Developments in Numerical Methods and Software for ODEs/DAEs/PDEs, G.D. Byrne and W.E. Schiesser, eds., World Scientific, Singapore, 1992, pp. 55-80.
    • (1992) Recent Developments in Numerical Methods and Software for ODEs/DAEs/PDEs , pp. 55-80
    • Flaherty, J.E.1    Wang, Y.2
  • 14
    • 0041732883 scopus 로고    scopus 로고
    • Finite difference methods and spatial a posteriori error estimates for solving parabolic equations in three space dimensions on grids with irregular nodes
    • P.K. MOORE, Finite difference methods and spatial a posteriori error estimates for solving parabolic equations in three space dimensions on grids with irregular nodes, SIAM J. Numer. Anal., 36 (1999), pp. 1044-1064.
    • (1999) SIAM J. Numer. Anal. , vol.36 , pp. 1044-1064
    • Moore, P.K.1
  • 15
    • 0030081174 scopus 로고    scopus 로고
    • A comparison of preconditioners in the solution of parabolic systems in three space dimensions using DASPK and a high order finite element method
    • P.K. MOORE AND R.H. DILLON, A comparison of preconditioners in the solution of parabolic systems in three space dimensions using DASPK and a high order finite element method, Appl. Numer. Math., 20 (1996), pp. 117-128.
    • (1996) Appl. Numer. Math. , vol.20 , pp. 117-128
    • Moore, P.K.1    Dillon, R.H.2
  • 16
    • 0000646363 scopus 로고
    • Comparison of adaptive methods for one-dimensional parabolic systems
    • P.K. MOORE, Comparison of adaptive methods for one-dimensional parabolic systems, Appl. Numer. Math., 16 (1995), pp. 471-488.
    • (1995) Appl. Numer. Math. , vol.16 , pp. 471-488
    • Moore, P.K.1
  • 17
    • 34250077980 scopus 로고
    • High-order adaptive finite element-singly implicit RungeKutta methods for parabolic differential equations
    • P.K. MOORE AND J.E. FLAHERTY, High-order adaptive finite element-singly implicit RungeKutta methods for parabolic differential equations, BIT, 33 (1993), pp. 309-331.
    • (1993) BIT , vol.33 , pp. 309-331
    • Moore, P.K.1    Flaherty, J.E.2
  • 18
    • 84985408358 scopus 로고
    • ILUT: A dual threshold incomplete LU factorization
    • Y. SAAD, ILUT: A dual threshold incomplete LU factorization, Numer. Linear Algebra Appl., 1 (1994), pp. 387-402.
    • (1994) Numer. Linear Algebra Appl. , vol.1 , pp. 387-402
    • Saad, Y.1
  • 19
    • 0000048673 scopus 로고
    • GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems
    • Y. SAAD AND M.H. SCHULTZ, GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Statist. Comput., 7 (1986), pp. 856-869.
    • (1986) SIAM J. Sci. Statist. Comput. , vol.7 , pp. 856-869
    • Saad, Y.1    Schultz, M.H.2
  • 20
    • 0039401067 scopus 로고
    • Local refinement of 3D-meshes consisting of prisms and conforming closure
    • K.G. SIEBERT, Local refinement of 3D-meshes consisting of prisms and conforming closure, Impact Comput. Sci. Engrg., 5 (1993), pp. 271-284.
    • (1993) Impact Comput. Sci. Engrg. , vol.5 , pp. 271-284
    • Siebert, K.G.1
  • 21
    • 0030530686 scopus 로고    scopus 로고
    • An a posteriori error estimator for anisotropic refinement
    • K.G. SIEBERT, An a posteriori error estimator for anisotropic refinement, Numer. Math., 73 (1996), pp. 373-398.
    • (1996) Numer. Math. , vol.73 , pp. 373-398
    • Siebert, K.G.1
  • 23
    • 0008441150 scopus 로고
    • Local-Mesh, Local-Order, Adaptive Finite Element Methods with a Posteriori Error Estimators for Elliptic Partial Differential Equations
    • Department of Computer Science, Yale University, New Haven, CT
    • A. WEISER, Local-Mesh, Local-Order, Adaptive Finite Element Methods with A Posteriori Error Estimators for Elliptic Partial Differential Equations, Tech. Report 213, Department of Computer Science, Yale University, New Haven, CT, 1981.
    • (1981) Tech. Report , vol.213
    • Weiser, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.