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Volumn 53, Issue 5, 2000, Pages 525-589

A posteriori error estimates for variable time-step discretizations of nonlinear evolution equations

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EID: 0034373609     PISSN: 00103640     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0312(200005)53:5<525::AID-CPA1>3.0.CO;2-M     Document Type: Article
Times cited : (164)

References (61)
  • 1
    • 0040717123 scopus 로고
    • Über die existenz und iterative berechnung einer lösung der Hammerstein'schen gleichung
    • Amann, H. Über die Existenz und iterative Berechnung einer Lösung der Hammerstein'schen Gleichung. Aequationes Math, 1 (1968), 242-266.
    • (1968) Aequationes Math , vol.1 , pp. 242-266
    • Amann, H.1
  • 3
    • 0039279366 scopus 로고
    • Quelques propriétés des opérateurs angle-bornés et n-cycliquement monotones
    • Baillon, J.-B.; Haddad, G. Quelques propriétés des opérateurs angle-bornés et n-cycliquement monotones. (French) Israel J. Math. 26 (1977), no. 2, 137-150.
    • (1977) Israel J. Math. , vol.26 , Issue.2 , pp. 137-150
    • Baillon, J.-B.1    Haddad, G.2
  • 4
    • 0002552584 scopus 로고
    • Discretization of evolution variational inequalities
    • Progr. Nonlinear Differential Equations Appl., 1. Birkhäuser Boston, Boston
    • Baiocchi, C. Discretization of evolution variational inequalities. Partial differential equations and the calculus of variations, Vol. I, 59-92. Progr. Nonlinear Differential Equations Appl., 1. Birkhäuser Boston, Boston, 1989.
    • (1989) Partial Differential Equations and the Calculus of Variations , vol.1 , pp. 59-92
    • Baiocchi, C.1
  • 5
    • 51249183467 scopus 로고
    • Optimal error estimates for linear parabolic problems under minimal regularity assumptions
    • Baiocchi, C.; Brezzi, F. Optimal error estimates for linear parabolic problems under minimal regularity assumptions. Calcolo 20 (1983), no. 2, 143-176.
    • (1983) Calcolo , vol.20 , Issue.2 , pp. 143-176
    • Baiocchi, C.1    Brezzi, F.2
  • 10
    • 0001312371 scopus 로고
    • Nonlinear integral equations and systems of Hammerstein type
    • Brézis, H.; Browder, F. E. Nonlinear integral equations and systems of Hammerstein type. Advances in Math. 18 (1975), no. 2, 115-147.
    • (1975) Advances in Math. , vol.18 , Issue.2 , pp. 115-147
    • Brézis, H.1    Browder, F.E.2
  • 11
    • 0001585127 scopus 로고
    • Sur la régularité de la solution d'inéquations elliptiques
    • Brezis, H. R.; Stampacchia, G. Sur la régularité de la solution d'inéquations elliptiques. (French) Bull. Soc. Math. France 96 (1968), 153-180.
    • (1968) Bull. Soc. Math. France , vol.96 , pp. 153-180
    • Brezis, H.R.1    Stampacchia, G.2
  • 13
    • 0031526904 scopus 로고    scopus 로고
    • The regularity of monotone maps of finite compression
    • Caffarelli, L. A. The regularity of monotone maps of finite compression. Comm. Pure Appl. Math. 50 (1997), no. 6, 563-591.
    • (1997) Comm. Pure Appl. Math. , vol.50 , Issue.6 , pp. 563-591
    • Caffarelli, L.A.1
  • 14
    • 0003211244 scopus 로고
    • Convex analysis and measurable multifunctions
    • Springer, Berlin-New York
    • Castaing, C.; Valadier, M. Convex analysis and measurable multifunctions. Lecture Notes in Mathematics, Vol. 580. Springer, Berlin-New York, 1977.
    • (1977) Lecture Notes in Mathematics , vol.580
    • Castaing, C.1    Valadier, M.2
  • 15
    • 0037849059 scopus 로고
    • Asymptotics for a parabolic double obstacle problem
    • Chen, X.; Elliott, C. M. Asymptotics for a parabolic double obstacle problem. Proc. Roy. Soc. London Ser. A 444 (1994), no. 1922, 429-445.
    • (1994) Proc. Roy. Soc. London Ser. A , vol.444 , Issue.1922 , pp. 429-445
    • Chen, X.1    Elliott, C.M.2
  • 17
    • 0038939216 scopus 로고    scopus 로고
    • Time discretization of Stefan problems with singular heat flux
    • Free boundary problems, theory and applications (Zakopane, 1995), Longman, Harlow
    • Colli, P; Savaré, G. Time discretization of Stefan problems with singular heat flux. Free boundary problems, theory and applications (Zakopane, 1995), 16-28. Pitman Res. Notes Math. Ser., 363. Longman, Harlow, 1996.
    • (1996) Pitman Res. Notes Math. Ser. , vol.363 , pp. 16-28
    • Colli, P.1    Savaré, G.2
  • 18
    • 0001274528 scopus 로고
    • Nonlinear semigroups and evolution governed by accretive operators
    • Nonlinear functional analysis and its applications, Part I (Berkeley, Calif., 1983), Amer. Math. Soc., Providence, R.I.
    • Crandall, M. G. Nonlinear semigroups and evolution governed by accretive operators. Nonlinear functional analysis and its applications, Part I (Berkeley, Calif., 1983), 305-337. Proc. Sympos. Pure Math., 45, Part 1. Amer. Math. Soc., Providence, R.I., 1986.
    • (1986) Proc. Sympos. Pure Math. , vol.45 , Issue.PART 1 , pp. 305-337
    • Crandall, M.G.1
  • 19
    • 51249191305 scopus 로고
    • On the relation of the operator ∂/∂s + ∂/∂τ to evolution governed by accretive operators
    • Crandall, M. G.; Evans, L. C. On the relation of the operator ∂/∂s + ∂/∂τ to evolution governed by accretive operators. Israel J. Math. 21 (1975), no. 4, 261-278.
    • (1975) Israel J. Math. , vol.21 , Issue.4 , pp. 261-278
    • Crandall, M.G.1    Evans, L.C.2
  • 20
    • 0000018252 scopus 로고
    • Generation of semi-groups of nonlinear transformations on general Banach spaces
    • Crandall, M. G.; Liggett, T. M. Generation of semi-groups of nonlinear transformations on general Banach spaces. Amer. J. Math. 93 (1971), 265-298.
    • (1971) Amer. J. Math. , vol.93 , pp. 265-298
    • Crandall, M.G.1    Liggett, T.M.2
  • 22
    • 0002945485 scopus 로고
    • Error analysis for a class of methods for stiff non-linear initial value problems
    • Numerical analysis (Proc. 6th Biennial Dundee Conf., Univ. Dundee, Dun-Dee, 1975), Springer, Berlin
    • Dahlquist, G. Error analysis for a class of methods for stiff non-linear initial value problems. Numerical analysis (Proc. 6th Biennial Dundee Conf., Univ. Dundee, Dun-Dee, 1975), 60-72. Lecture Notes in Mathematics, Vol. 506, Springer, Berlin, 1976.
    • (1976) Lecture Notes in Mathematics , vol.506 , pp. 60-72
    • Dahlquist, G.1
  • 23
    • 0000137841 scopus 로고
    • Subdifferential operator approach to a class of nonlinear systems for stefan problems with phase relaxation
    • Damlamian, A.; Kenmochi, N.; Sato, N. Subdifferential operator approach to a class of nonlinear systems for Stefan problems with phase relaxation. Nonlinear Anal. 23 (1994), no. 1, 115-142.
    • (1994) Nonlinear Anal. , vol.23 , Issue.1 , pp. 115-142
    • Damlamian, A.1    Kenmochi, N.2    Sato, N.3
  • 24
    • 0000161576 scopus 로고
    • Geometrical evolution of developed interfaces
    • de Mottoni, P.; Schatzman, M. Geometrical evolution of developed interfaces. Trans. Amer. Math. Soc. 347 (1995), no. 5, 1533-1589.
    • (1995) Trans. Amer. Math. Soc. , vol.347 , Issue.5 , pp. 1533-1589
    • De Mottoni, P.1    Schatzman, M.2
  • 26
    • 0003663617 scopus 로고
    • (French) Collection Etudes Mathématiques. Dunod; Gauthier-Villars, Paris-Brussels-Montreal
    • Ekeland, I.; Temam, R. Analyse convexe et problèmes variationnels. (French) Collection Etudes Mathématiques. Dunod; Gauthier-Villars, Paris-Brussels-Montreal, 1974.
    • (1974) Analyse Convexe et Problèmes Variationnels
    • Ekeland, I.1    Temam, R.2
  • 28
    • 0026106415 scopus 로고
    • Adaptive finite element methods for parabolic problems. I. A linear model problem
    • Eriksson, K.; Johnson, C. Adaptive finite element methods for parabolic problems. I. A linear model problem. SIAM J. Numer. Anal. 28 (1991), no. 1, 43-77.
    • (1991) SIAM J. Numer. Anal. , vol.28 , Issue.1 , pp. 43-77
    • Eriksson, K.1    Johnson, C.2
  • 29
    • 84904150653 scopus 로고
    • Adaptive finite element methods for parabolic problems. IV. Nonlinear problems
    • Eriksson, K.; Johnson, C. Adaptive finite element methods for parabolic problems. IV. Nonlinear problems. SIAM J. Numer. Anal. 32 (1995), no. 6, 1729-1749.
    • (1995) SIAM J. Numer. Anal. , vol.32 , Issue.6 , pp. 1729-1749
    • Eriksson, K.1    Johnson, C.2
  • 30
    • 0001648207 scopus 로고    scopus 로고
    • Adaptive finite element methods for parabolic problems. VI. Analytic semigroups
    • electronic
    • Eriksson, K.; Johnson, C.; Larsson, S. Adaptive finite element methods for parabolic problems. VI. Analytic semigroups. SIAM J. Numer. Anal. 35 (1998), no. 4, 1315-1325 (electronic).
    • (1998) SIAM J. Numer. Anal. , vol.35 , Issue.4 , pp. 1315-1325
    • Eriksson, K.1    Johnson, C.2    Larsson, S.3
  • 32
    • 0003343498 scopus 로고
    • Minimal surfaces and functions of bounded variation
    • Birkhäuser, Basel-Boston
    • Giusti, E. Minimal surfaces and functions of bounded variation. Monographs in Mathematics, 80. Birkhäuser, Basel-Boston, 1984.
    • (1984) Monographs in Mathematics , vol.80
    • Giusti, E.1
  • 34
    • 0003320921 scopus 로고
    • Elliptic problems in nonsmooth domains
    • Pitman (Advanced Publishing Program), Boston-London
    • Grisvard, P. Elliptic problems in nonsmooth domains. Monographs and Studies in Mathematics, 24. Pitman (Advanced Publishing Program), Boston-London, 1985.
    • (1985) Monographs and Studies in Mathematics , vol.24
    • Grisvard, P.1
  • 35
    • 0001449110 scopus 로고    scopus 로고
    • Solving ordinary differential equations. II. Stiff and differential-algebraic problems. Second edition
    • Springer, Berlin
    • Hairer, E.; Wanner, G. Solving ordinary differential equations. II. Stiff and differential-algebraic problems. Second edition. Springer Series in Computational Mathematics, 14. Springer, Berlin, 1996.
    • (1996) Springer Series in Computational Mathematics , vol.14
    • Hairer, E.1    Wanner, G.2
  • 37
    • 0001562231 scopus 로고
    • Error estimates and adaptive time-step control for a class of one-step methods for stiff ordinary differential equations
    • Johnson, C. Error estimates and adaptive time-step control for a class of one-step methods for stiff ordinary differential equations. SIAM J. Numer. Anal. 25 (1988), no. 4, 908-926.
    • (1988) SIAM J. Numer. Anal. , vol.25 , Issue.4 , pp. 908-926
    • Johnson, C.1
  • 38
    • 0039531750 scopus 로고
    • Perturbation theory for linear operators. Second edition
    • Springer, Berlin-New York
    • Kato, T. Perturbation theory for linear operators. Second edition. Grundlehren der Mathematischen Wissenschaften, Band 132. Springer, Berlin-New York, 1976.
    • (1976) Grundlehren der Mathematischen Wissenschaften , vol.132
    • Kato, T.1
  • 39
    • 0003235422 scopus 로고
    • Systems of nonlinear PDEs arising from dynamical phase transitions
    • Phase transitions and hysteresis (Montecatini Terme, 1993), Springer, Berlin
    • Kenmochi, N. Systems of nonlinear PDEs arising from dynamical phase transitions. Phase transitions and hysteresis (Montecatini Terme, 1993), 39-86. Lecture Notes in Mathematics, 1584. Springer, Berlin, 1994.
    • (1994) Lecture Notes in Mathematics , vol.1584 , pp. 39-86
    • Kenmochi, N.1
  • 40
    • 0003295459 scopus 로고
    • An introduction to variational inequalities and their applications
    • Academic Press [Harcourt Brace Jovanovich], New York-London
    • Kinderlehrer, D.; Stampacchia, G. An introduction to variational inequalities and their applications. Pure and Applied Mathematics, 88. Academic Press [Harcourt Brace Jovanovich], New York-London, 1980.
    • (1980) Pure and Applied Mathematics , vol.88
    • Kinderlehrer, D.1    Stampacchia, G.2
  • 41
    • 0000858276 scopus 로고
    • Pseudosolutions of the time-dependent minimal surface problem
    • Lichnewsky, A.; Temam, R. Pseudosolutions of the time-dependent minimal surface problem. J. Differential Equations 30 (1978), no. 3, 340-364.
    • (1978) J. Differential Equations , vol.30 , Issue.3 , pp. 340-364
    • Lichnewsky, A.1    Temam, R.2
  • 46
    • 0003246772 scopus 로고
    • Multiple integrals in the calculus of variations
    • Springer New York, New York
    • Morrey, C. B., Jr. Multiple integrals in the calculus of variations. Die Grundlehren der mathematischen Wissenschaften, Band 130. Springer New York, New York, 1966.
    • (1966) Die Grundlehren der Mathematischen Wissenschaften , vol.130
    • Morrey C.B., Jr.1
  • 48
    • 84979525634 scopus 로고    scopus 로고
    • Adaptive solution of phase change problems over unstructured tetrahedral meshes
    • Grid generation and adaptive algorithms, Springer, New York
    • Nochetto, R. H.; Schmidt, A.; Verdi, C. Adaptive solution of phase change problems over unstructured tetrahedral meshes. Grid generation and adaptive algorithms, 163-181. The IMA Volumes in Mathematics and Its Applications, 113. Springer, New York, 1999.
    • (1999) The IMA Volumes in Mathematics and Its Applications , vol.113 , pp. 163-181
    • Nochetto, R.H.1    Schmidt, A.2    Verdi, C.3
  • 49
    • 0034424235 scopus 로고    scopus 로고
    • A posteriori error estimation and adaptivity for degenerate parabolic problems
    • Nochetto, R. H.; Schmidt, A.; Verdi, C. A posteriori error estimation and adaptivity for degenerate parabolic problems. Math. Comp. 69 (2000), no. 229, 1-24.
    • (2000) Math. Comp. , vol.69 , Issue.229 , pp. 1-24
    • Nochetto, R.H.1    Schmidt, A.2    Verdi, C.3
  • 50
    • 84972545670 scopus 로고
    • Characterization of the subdifferentials of convex functions
    • Rockafellar, R. T. Characterization of the subdifferentials of convex functions. Pacific J. Math. 17 (1966), 497-510.
    • (1966) Pacific J. Math. , vol.17 , pp. 497-510
    • Rockafellar, R.T.1
  • 51
    • 0004267646 scopus 로고
    • Princeton Mathematical Series, No. 28. Princeton University Press, Princeton, N.J.
    • Rockafellar, R. T. Convex analysis. Princeton Mathematical Series, No. 28. Princeton University Press, Princeton, N.J., 1970.
    • (1970) Convex Analysis
    • Rockafellar, R.T.1
  • 52
    • 0001779231 scopus 로고    scopus 로고
    • Error analysis for implicit approximations to solutions to Cauchy problems
    • Rulla, J. Error analysis for implicit approximations to solutions to Cauchy problems. SIAM J. Numer. Anal. 33 (1996), no. 1, 68-87.
    • (1996) SIAM J. Numer. Anal. , vol.33 , Issue.1 , pp. 68-87
    • Rulla, J.1
  • 53
    • 0038939215 scopus 로고
    • Approximation and regularity of evolution variational inequalities
    • Savaré, G. Approximation and regularity of evolution variational inequalities. Rend. Accad. Naz. Sci. XL Mem. Mat. (5) 17 (1993), 83-111.
    • (1993) Rend. Accad. Naz. Sci. XL Mem. Mat. (5) , vol.17 , pp. 83-111
    • Savaré, G.1
  • 54
    • 0000616291 scopus 로고    scopus 로고
    • Weak solutions and maximal regularity for abstract evolution inequalities
    • Savaré, G. Weak solutions and maximal regularity for abstract evolution inequalities. Adv. Math. Sci. Appl. 6 (1996), no. 2, 377-418.
    • (1996) Adv. Math. Sci. Appl. , vol.6 , Issue.2 , pp. 377-418
    • Savaré, G.1
  • 55
    • 0002592744 scopus 로고    scopus 로고
    • Regularity results for elliptic equations in Lipschitz domains
    • Savaré, G. Regularity results for elliptic equations in Lipschitz domains. J. Funct. Anal. 152 (1998), no. 1, 176-201.
    • (1998) J. Funct. Anal. , vol.152 , Issue.1 , pp. 176-201
    • Savaré, G.1
  • 56
    • 0039796448 scopus 로고    scopus 로고
    • Variational convergence of nonlinear diffusion equations: Applications to concentrated capacity problems with change of phase
    • Savaré, G.; Visintin, A. Variational convergence of nonlinear diffusion equations: applications to concentrated capacity problems with change of phase. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 8 (1997), no. 1, 49-89.
    • (1997) Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. , vol.8 , Issue.1 , pp. 49-89
    • Savaré, G.1    Visintin, A.2
  • 57
    • 0012145462 scopus 로고
    • Solutions généralisées de certaines équations du type hypersurfaces minima
    • Temam, R. Solutions généralisées de certaines équations du type hypersurfaces minima. (French) Arch. Rational Mech. Anal. 44 (1971/72), 121-156.
    • (1971) Arch. Rational Mech. Anal. , vol.44 , pp. 121-156
    • Temam, R.1
  • 58
    • 0040123233 scopus 로고
    • Applications de l'analyse convexe au calcul des variations
    • Springer, Berlin
    • Temam, R. Applications de l'analyse convexe au calcul des variations. (French) Nonlinear operators and the calculus of variations (Summer School, Univ. Libre Bruxelles, Brussels, 1975), 208-237. Lecture Notes in Mathematics, Vol. 543, Springer, Berlin, 1976.
    • (1976) Lecture Notes in Mathematics , vol.543 , pp. 208-237
    • Temam, R.1
  • 59
    • 0003345958 scopus 로고    scopus 로고
    • Galerkin finite element methods for parabolic problems
    • Springer, Berlin
    • Thomée, V. Galerkin finite element methods for parabolic problems. Springer Series in Computational Mathematics, 25. Springer, Berlin, 1997.
    • (1997) Springer Series in Computational Mathematics , vol.25
    • Thomée, V.1
  • 60
    • 0039531751 scopus 로고
    • Regularity theorems and optimal error estimates for linear parabolic Cauchy problems
    • Tomarelli, F. Regularity theorems and optimal error estimates for linear parabolic Cauchy problems. Numer. Math. 45 (1984), no. 1, 23-50.
    • (1984) Numer. Math. , vol.45 , Issue.1 , pp. 23-50
    • Tomarelli, F.1
  • 61
    • 0001123368 scopus 로고
    • Stefan problem with phase relaxation
    • Visintin, A. Stefan problem with phase relaxation. IMA J. Appl. Math. 34 (1985), no. 3, 225-245.
    • (1985) IMA J. Appl. Math. , vol.34 , Issue.3 , pp. 225-245
    • Visintin, A.1


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