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Volumn 36, Issue 3, 1999, Pages 974-999

A P1 - P1 finite element method for a phase relaxation model II: Adaptively refined meshes

Author keywords

Diffuse interface; Double obstacle; Graded meshes; Numerical integration; Phase relaxation; Piecewise linear finite elements

Indexed keywords


EID: 0003344020     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142997317596     Document Type: Article
Times cited : (7)

References (22)
  • 1
    • 38249010485 scopus 로고
    • The existence of weak solutions to single porosity and simple dual-porosity models of two-phase incompressible flow
    • T. ARBOGAST, The existence of weak solutions to single porosity and simple dual-porosity models of two-phase incompressible flow, Nonlinear Anal. 19 (1992), pp. 1009-1031.
    • (1992) Nonlinear Anal. , vol.19 , pp. 1009-1031
    • Arbogast, T.1
  • 3
    • 0025227045 scopus 로고
    • The dynamics of a conserved phase field system: Stefan-like, Hele-Shaw, and Cahn-Hilliard models as asymptotic limits
    • G. CAGINALP, The dynamics of a conserved phase field system: Stefan-like, Hele-Shaw, and Cahn-Hilliard models as asymptotic limits, IMA J. Appl. Math, 44 (1990), pp. 77-94.
    • (1990) IMA J. Appl. Math , vol.44 , pp. 77-94
    • Caginalp, G.1
  • 5
    • 0002214041 scopus 로고
    • Maximum principle and uniform convergence for the finite element method
    • P. G. CIARLET AND P.-A. RAVIART, Maximum principle and uniform convergence for the finite element method, Comput. Methods Appl. Mech. Engrg., 2 (1973), pp. 17-31.
    • (1973) Comput. Methods Appl. Mech. Engrg. , vol.2 , pp. 17-31
    • Ciarlet, P.G.1    Raviart, P.-A.2
  • 6
    • 0026487791 scopus 로고
    • Travelling waves in the transport of reactive solutes through porous media: Adsorption and binary ion exchanges. Part I
    • C. N. VAN DUIJN AND P. KNABNER, Travelling waves in the transport of reactive solutes through porous media: Adsorption and binary ion exchanges. Part I, Transport in Porous Media, 8 (1992), pp. 167-184.
    • (1992) Transport in Porous Media , vol.8 , pp. 167-184
    • Van Duijn, C.N.1    Knabner, P.2
  • 8
    • 84966199242 scopus 로고
    • Error estimates for the multidimentional two-phase Stefan problem
    • J. W. JEROME AND M. E. ROSE, Error estimates for the multidimentional two-phase Stefan problem, Math. Comp., 39 (1982), pp. 377-414.
    • (1982) Math. Comp. , vol.39 , pp. 377-414
    • Jerome, J.W.1    Rose, M.E.2
  • 10
    • 0040360888 scopus 로고    scopus 로고
    • Optimal error estimates for semidiscrete phase relaxation models
    • X. JIANG AND R. H. NOCHETTO, Optimal error estimates for semidiscrete phase relaxation models, RAIRO Model. Math. Anal. Numer., 31 (1997), pp. 91-120.
    • (1997) RAIRO Model. Math. Anal. Numer. , vol.31 , pp. 91-120
    • Jiang, X.1    Nochetto, R.H.2
  • 11
    • 0039706872 scopus 로고    scopus 로고
    • 1 finite element method for a phase relaxation model. Part I: Quasi-uniform mesh
    • 1 finite element method for a phase relaxation model. Part I: Quasi-uniform mesh, SIAM J. Numer. Anal., 35 (1998), pp. 1176-1190.
    • (1998) SIAM J. Numer. Anal. , vol.35 , pp. 1176-1190
    • Jiang, X.1    Nochetto, R.H.2
  • 13
    • 84966202728 scopus 로고
    • An adaptive finite element method for two-phase Stefan problems in two space dimensions. Part I: Stability and error estimates
    • R. H. NOCHETTO, M. PAOLINI, AND C. VERDI, An adaptive finite element method for two-phase Stefan problems in two space dimensions. Part I: Stability and error estimates, Math. Comp., 57 (1991), pp. 73-108. Supplement, Math. Comp., 57 (1991), pp. S1-S11.
    • (1991) Math. Comp. , vol.57 , pp. 73-108
    • Nochetto, R.H.1    Paolini, M.2    Verdi, C.3
  • 14
    • 84966202728 scopus 로고
    • R. H. NOCHETTO, M. PAOLINI, AND C. VERDI, An adaptive finite element method for two- phase Stefan problems in two space dimensions. Part I: Stability and error estimates, Math. Comp., 57 (1991), pp. 73-108. Supplement, Math. Comp., 57 (1991), pp. S1-S11.
    • (1991) Supplement, Math. Comp. , vol.57
  • 15
    • 0001504699 scopus 로고
    • An adaptive finite element method for two-phase Stefan problems in two space dimensions. Part II: Implementation and numerical experiments
    • R. H. NOCHETTO, M. PAOLINI, AND C. VERDI, An adaptive finite element method for two-phase Stefan problems in two space dimensions. Part II: Implementation and numerical experiments, SIAM J. Sci. Statist. Comput., 12 (1991), pp. 1207-1244.
    • (1991) SIAM J. Sci. Statist. Comput. , vol.12 , pp. 1207-1244
    • Nochetto, R.H.1    Paolini, M.2    Verdi, C.3
  • 16
    • 0027642683 scopus 로고
    • A fully discrete adaptive nonlinear Chernoff formula
    • R. H. NOCHETTO, M. PAOLINI, AND C. VERDI, A fully discrete adaptive nonlinear Chernoff formula, SIAM J. Numer. Anal., 30 (1993), pp. 991-1014.
    • (1993) SIAM J. Numer. Anal. , vol.30 , pp. 991-1014
    • Nochetto, R.H.1    Paolini, M.2    Verdi, C.3
  • 17
    • 84974315674 scopus 로고
    • Continuous and semidiscrete travelling waves for a phase relaxation model
    • R. H. NOCHETTO, M. PAOLINI, AND C. VERDI, Continuous and semidiscrete travelling waves for a phase relaxation model, European J. Appl. Math., 5 (1994), pp. 177-199.
    • (1994) European J. Appl. Math. , vol.5 , pp. 177-199
    • Nochetto, R.H.1    Paolini, M.2    Verdi, C.3
  • 18
    • 0011504510 scopus 로고
    • An automatic mesh generator for planar domain
    • M. PAOLINI AND C. VERDI, An automatic mesh generator for planar domain, Riv. Inform., 20 (1990), pp. 251-267.
    • (1990) Riv. Inform. , vol.20 , pp. 251-267
    • Paolini, M.1    Verdi, C.2
  • 19
    • 0041139652 scopus 로고
    • Numerical analysis of the multidimensional Stefan problem with supercooling and superheating
    • C. VERDI AND A. VISINTIN, Numerical analysis of the multidimensional Stefan problem with supercooling and superheating, Boll. Un. Mat. Ital. B(7), 1 (1987), pp. 795-814.
    • (1987) Boll. Un. Mat. Ital. B(7) , vol.1 , pp. 795-814
    • Verdi, C.1    Visintin, A.2
  • 20
    • 0002361341 scopus 로고
    • Error estimates for a semi-explicit numerical scheme for Stefan-type problems
    • C. VERDI AND A. VISINTIN, Error estimates for a semi-explicit numerical scheme for Stefan-type problems, Numer. Math., 52 (1988), pp. 165-185.
    • (1988) Numer. Math. , vol.52 , pp. 165-185
    • Verdi, C.1    Visintin, A.2
  • 21
    • 0001123368 scopus 로고
    • Stefan problem with phase relaxation
    • A. VISINTIN, Stefan problem with phase relaxation, IMA. J. Appl. Math., 34 (1985), pp. 225-245.
    • (1985) IMA. J. Appl. Math. , vol.34 , pp. 225-245
    • Visintin, A.1
  • 22
    • 0002360354 scopus 로고
    • Supercooling and superheating effects in phase transitions
    • A. VISINTIN, Supercooling and superheating effects in phase transitions, IMA J. Appl. Math, 35 (1985), pp. 233-256.
    • (1985) IMA J. Appl. Math , vol.35 , pp. 233-256
    • Visintin, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.