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Volumn 38, Issue 1, 2004, Pages 129-142

A posteriori error control for the Allen-Cahn problem: Circumventing Gronwall's inequality

Author keywords

A posteriori error estimates; Adaptive finite element method; Phase field models

Indexed keywords


EID: 1342283759     PISSN: 0764583X     EISSN: None     Source Type: Journal    
DOI: 10.1051/m2an:2004006     Document Type: Article
Times cited : (103)

References (12)
  • 1
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    • A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening
    • S.M. Allen and J.W. Cahn, A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening. Acta Metall. 27 (1979) 1085-1095.
    • (1979) Acta Metall. , vol.27 , pp. 1085-1095
    • Allen, S.M.1    Cahn, J.W.2
  • 3
    • 0032327786 scopus 로고    scopus 로고
    • Convergence of the phase-field model to its sharp interface limits
    • G. Caginalp and X. Chen, Convergence of the phase-field model to its sharp interface limits. Euro. J. Appl. Math. 9 (1998) 417-445.
    • (1998) Euro. J. Appl. Math. , vol.9 , pp. 417-445
    • Caginalp, G.1    Chen, X.2
  • 4
    • 0542363944 scopus 로고
    • Spectrum for the Allen-Cahn, Cahn-Hilliard, and phase-field equations for generic interfaces
    • X. Chen, Spectrum for the Allen-Cahn, Cahn-Hilliard, and phase-field equations for generic interfaces. Comm. Partial Differantial Equations 19 (1994) 1371-1395.
    • (1994) Comm. Partial Differantial Equations , vol.19 , pp. 1371-1395
    • Chen, X.1
  • 5
    • 0016541865 scopus 로고
    • Approximation by finite element functions using local regularization
    • Ph. Clément, Approximation by finite element functions using local regularization. RAIRO Anal. Numér 9 (1975) 77-84.
    • (1975) RAIRO Anal. Numér , vol.9 , pp. 77-84
    • Clément, Ph.1
  • 7
    • 0000161576 scopus 로고
    • Geometrical evolution of developed interfaces
    • P. de Mottoni and M. Schatzman, Geometrical evolution of developed interfaces. Trans. Amer. Math. Soc. 347 (1995) 1533-1589.
    • (1995) Trans. Amer. Math. Soc. , vol.347 , pp. 1533-1589
    • De Mottoni, P.1    Schatzman, M.2
  • 8
    • 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) 1729-1749.
    • (1995) SIAM J. Numer. Anal. , vol.32 , pp. 1729-1749
    • Eriksson, K.1    Johnson, C.2
  • 9
    • 0142087018 scopus 로고    scopus 로고
    • Numerical analysis of the Allen-Cahn equation and approximation for mean curvature flows
    • X. Feng and A. Prohl, Numerical analysis of the Allen-Cahn equation and approximation for mean curvature flows. Num. Math. 94 (2003) 33-65.
    • (2003) Num. Math. , vol.94 , pp. 33-65
    • Feng, X.1    Prohl, A.2
  • 10
    • 1342297216 scopus 로고    scopus 로고
    • Elliptic reconstruction and a posteriori error estimates for parabolic problems
    • Ch. Makridakis and R.H. Nochetto, Elliptic reconstruction and a posteriori error estimates for parabolic problems. SIAM J. Numer. Anal. 41 (2003) 1585-1594.
    • (2003) SIAM J. Numer. Anal. , vol.41 , pp. 1585-1594
    • Makridakis, Ch.1    Nochetto, R.H.2
  • 11
    • 0034171488 scopus 로고    scopus 로고
    • Existence of solutions to a phase-field model for the solidification process of a binary alloy
    • J. Rappaz and J.-F. Scheid, Existence of solutions to a phase-field model for the solidification process of a binary alloy. Math. Methods Appl. Sci. 23 (2000) 491-513.
    • (2000) Math. Methods Appl. Sci. , vol.23 , pp. 491-513
    • Rappaz, J.1    Scheid, J.-F.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.