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Volumn 91, Issue 2, 2002, Pages 197-222

A mixed finite element method for nonlinear elasticity: Two-fold saddle point approach and a-posteriori error estimate

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EID: 0036013090     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002110100337     Document Type: Article
Times cited : (48)

References (40)
  • 1
    • 0040040139 scopus 로고    scopus 로고
    • Estimateur d'erreur a posteriori hiérarchique. Application aux éléments finis mixtes
    • Achchab, B., Agouzal, A., Baranger, J., Maitre, J.F.: Estimateur d'Erreur a posteriori hiérarchique. Application aux éléments finis mixtes. Numerische Mathematik 80, 159-179 (1998)
    • (1998) Numerische Mathematik , vol.80 , pp. 159-179
    • Achchab, B.1    Agouzal, A.2    Baranger, J.3    Maitre, J.F.4
  • 2
    • 0042255750 scopus 로고
    • A unified approach to a posteriori error estimation using element residual methods
    • Ainsworth, M., Oden, J.T.: A unified approach to a posteriori error estimation using element residual methods. Numerische Mathematik 65, 23-50 (1993)
    • (1993) Numerische Mathematik , vol.65 , pp. 23-50
    • Ainsworth, M.1    Oden, J.T.2
  • 3
    • 0001309064 scopus 로고    scopus 로고
    • A posteriori error estimators for the Stokes and Oseen equations
    • Ainsworth, M., Oden, J.T.: A posteriori error estimators for the Stokes and Oseen equations. SIAM. J. Numerical Anal 34, 228-245 (1997)
    • (1997) SIAM. J. Numerical Anal. , vol.34 , pp. 228-245
    • Ainsworth, M.1    Oden, J.T.2
  • 4
    • 0031102111 scopus 로고    scopus 로고
    • A posteriori error estimation in finite element analysis
    • Ainsworth, M., Oden, J.T.: A posteriori error estimation in finite element analysis. Comput Methods Appl. Mech. Eng. 142, 1-88 (1997)
    • (1997) Comput. Methods Appl. Mech. Eng. , vol.142 , pp. 1-88
    • Ainsworth, M.1    Oden, J.T.2
  • 5
    • 0030506843 scopus 로고    scopus 로고
    • Error estimators for a mixed method
    • Alonso, A.: Error estimators for a mixed method. Numerische Mathematik 74, 385-395 (1996)
    • (1996) Numerische Mathematik , vol.74 , pp. 385-395
    • Alonso, A.1
  • 6
    • 0030125361 scopus 로고    scopus 로고
    • A boundary-field equation method for a nonlinear exterior elasticity problem in the plane
    • Araya, R.A., Gatica, G.N., Mennickent, H.: A boundary-field equation method for a nonlinear exterior elasticity problem in the plane. J. Elasticity 43, 45-68 (1996)
    • (1996) J. Elasticity , vol.43 , pp. 45-68
    • Araya, R.A.1    Gatica, G.N.2    Mennickent, H.3
  • 7
    • 0000369744 scopus 로고
    • PEERS: A new mixed finite element for plane elasticity
    • Arnold, D.N., Brezzi, F., Douglas, J.: PEERS: A new mixed finite element for plane elasticity. Jpn. J. Appl. Math. 1, 347-367 (1984)
    • (1984) Jpn. J. Appl. Math. , vol.1 , pp. 347-367
    • Arnold, D.N.1    Brezzi, F.2    Douglas, J.3
  • 8
    • 0027642848 scopus 로고
    • A posteriori error estimates based on hierarchical bases
    • Bank, R.E., Smith, R.: A posteriori error estimates based on hierarchical bases. SIAM. J. Numerical Anal. 30, 921-935 (1993)
    • (1993) SIAM. J. Numerical Anal. , vol.30 , pp. 921-935
    • Bank, R.E.1    Smith, R.2
  • 9
    • 84966215690 scopus 로고
    • Some a posteriori error estimators for elliptic partial differential equations
    • Bank, R.E., Weiser, A.: Some a posteriori error estimators for elliptic partial differential equations. Math. Comput. 44, 283-301 (1985)
    • (1985) Math. Comput. , vol.44 , pp. 283-301
    • Bank, R.E.1    Weiser, A.2
  • 10
    • 0000518260 scopus 로고    scopus 로고
    • A posteriori error estimators for the Raviart-Thomas element
    • Braess, D., Verfürth, R.: A posteriori error estimators for the Raviart-Thomas element. SIAM. J. Numerical Anal. 33, 2431-2444 (1996)
    • (1996) SIAM. J. Numerical Anal. , vol.33 , pp. 2431-2444
    • Braess, D.1    Verfürth, R.2
  • 12
    • 0032479720 scopus 로고    scopus 로고
    • A posteriori error estimation in large-strain elasticity using equilibrated local Neumann problems
    • Brink, U., Stein, E.: A posteriori error estimation in large-strain elasticity using equilibrated local Neumann problems. Comput. Methods Appl. Mech. Eng. 161, 77-101 (1998)
    • (1998) Comput. Methods Appl. Mech. Eng. , vol.161 , pp. 77-101
    • Brink, U.1    Stein, E.2
  • 13
    • 0000365439 scopus 로고    scopus 로고
    • Implicit residual error estimators for the coupling of finite elements and boundary elements
    • Brink, U., Stephan, E.P.; Implicit residual error estimators for the coupling of finite elements and boundary elements. Math. Methods Appl. Sci. 22, 923-936 (1999)
    • (1999) Math. Methods Appl. Sci. , vol.22 , pp. 923-936
    • Brink, U.1    Stephan, E.P.2
  • 14
    • 0001997743 scopus 로고    scopus 로고
    • Adaptive coupling of boundary elements and mixed finite elements for incompressible elasticity
    • Brink, U., Stephan, E.P.: Adaptive coupling of boundary elements and mixed finite elements for incompressible elasticity. Numerical Methods Partial Diff. Eqs. 17, 79-92 (2001)
    • (2001) Numerical Methods Partial Diff. Eqs. , vol.17 , pp. 79-92
    • Brink, U.1    Stephan, E.P.2
  • 15
    • 0031491856 scopus 로고    scopus 로고
    • A-posteriori error estimate for the mixed finite element method
    • Carstensen, C.: A-posteriori error estimate for the mixed finite element method. Math. Comput. 66, 465-476 (1997)
    • (1997) Math. Comput. , vol.66 , pp. 465-476
    • Carstensen, C.1
  • 16
    • 0039992460 scopus 로고    scopus 로고
    • Expanded mixed finite element methods for linear second-order elliptic problems
    • Chen, Z.: Expanded mixed finite element methods for linear second-order elliptic problems. Math. Modelling Numerical Anal. 32, 479-499 (1998)
    • (1998) Math. Modelling Numerical Anal. , vol.32 , pp. 479-499
    • Chen, Z.1
  • 17
    • 0032369306 scopus 로고    scopus 로고
    • Expanded mixed finite element methods for quasilinear second-order elliptic problems
    • Chen, Z.: Expanded mixed finite element methods for quasilinear second-order elliptic problems. Math. Modelling Numerical Anal. 32, 501-520 (1998)
    • (1998) Math. Modelling Numerical Anal. , vol.32 , pp. 501-520
    • Chen, Z.1
  • 21
    • 0035579499 scopus 로고    scopus 로고
    • Minimum residual iteration for a dual-dual mixed formulation of exterior transmission problems
    • Gatica, G.N., Heuer, N.: Minimum residual iteration for a dual-dual mixed formulation of exterior transmission problems. Numerical Linear Algebra Appl. 8, 3, 147-164 (2001)
    • (2001) Numerical Linear Algebra Appl. , vol.8 , Issue.3 , pp. 147-164
    • Gatica, G.N.1    Heuer, N.2
  • 22
    • 0035879360 scopus 로고    scopus 로고
    • An expanded mixed finite element approach via a dual-dual formulation and the minimum residual method
    • Gatica, G.N., Heuer, N.: An expanded mixed finite element approach via a dual-dual formulation and the minimum residual method. J. Comput. Applied Math. 132, 2, 371-385 (2001).
    • (2001) J. Comput. Applied Math. , vol.132 , Issue.2 , pp. 371-385
    • Gatica, G.N.1    Heuer, N.2
  • 23
    • 0012916119 scopus 로고    scopus 로고
    • Conjugate gradient method for dual-dual mixed formulations
    • Technical Report 99-16, Departamento de Ingeniería Matemática, Universidad de Concepción
    • Gatica, G.N., Heuer, N.: Conjugate gradient method for dual-dual mixed formulations. Technical Report 99-16, Departamento de Ingeniería Matemática, Universidad de Concepción (1999). To appear in Math. Comput.
    • (1999) Math. Comput.
    • Gatica, G.N.1    Heuer, N.2
  • 24
    • 0034446066 scopus 로고    scopus 로고
    • A dual-dual formulation for the coupling of mixed-FEM and BEM in hyperelasticity
    • Gatica, G.N., Heuer, N.: A dual-dual formulation for the coupling of mixed-FEM and BEM in hyperelasticity. SIAM. J. Numerical Anal. 38, 2, 380-400 (2000)
    • (2000) SIAM. J. Numerical Anal. , vol.38 , Issue.2 , pp. 380-400
    • Gatica, G.N.1    Heuer, N.2
  • 25
    • 0002581406 scopus 로고
    • On a class of variational formulations for some nonlinear interface problems
    • Gatica, G.N., Hsiao, G.C.: On a class of variational formulations for some nonlinear interface problems. Rendiconti di Matemática e délle sue Applicazione 10(4), 681-715 (1990)
    • (1990) Rendiconti di Matemática e délle sue Applicazione , vol.10 , Issue.4 , pp. 681-715
    • Gatica, G.N.1    Hsiao, G.C.2
  • 26
    • 0003358109 scopus 로고    scopus 로고
    • A dual-dual mixed formulation for nonlinear exterior transmission problems
    • posted on May 23, PII S 0025-5718(00)01267-9 (to appear in print)
    • Gatica, G.N., Meddahi, S: A dual-dual mixed formulation for nonlinear exterior transmission problems. Math. Comput., posted on May 23, 2000, PII S 0025-5718(00)01267-9 (to appear in print)
    • (2000) Math. Comput.
    • Gatica, G.N.1    Meddahi, S.2
  • 27
    • 0002980012 scopus 로고    scopus 로고
    • Coupling of mixed finite elements and boundary elements for linear and nonlinear elliptic problems
    • Gatica, G.N., Wendland, W.L.: Coupling of mixed finite elements and boundary elements for linear and nonlinear elliptic problems. Appl. Anal. 63, 39-75 (1996)
    • (1996) Appl. Anal. , vol.63 , pp. 39-75
    • Gatica, G.N.1    Wendland, W.L.2
  • 28
    • 0000850520 scopus 로고    scopus 로고
    • Coupling of mixed finite elements and boundary elements for a hyperelastic interface problem
    • Gatica, G.N., Wendland, W.L.: Coupling of mixed finite elements and boundary elements for a hyperelastic interface problem. SIAM. J. Numerical Anal. 34(6), 2335-2356 (1997)
    • (1997) SIAM. J. Numerical Anal. , vol.34 , Issue.6 , pp. 2335-2356
    • Gatica, G.N.1    Wendland, W.L.2
  • 30
    • 0012960009 scopus 로고    scopus 로고
    • Some observations on mixed methods for fully nonlinear parabolic problems in divergence forms
    • Kim, M.Y., Milner, F.A., Park, E.J.: Some observations on mixed methods for fully nonlinear parabolic problems in divergence forms. Appl. Math. Lett. 9, 75-81 (1996)
    • (1996) Appl. Math. Lett. , vol.9 , pp. 75-81
    • Kim, M.Y.1    Milner, F.A.2    Park, E.J.3
  • 31
    • 0000348378 scopus 로고    scopus 로고
    • Mixed finite element methods for nonlinear elliptic problems: The p-version
    • Lee, M., Milner, F.A.: Mixed finite element methods for nonlinear elliptic problems: the p-version. Numerical Methods Partial Diff. Eqs. 12, 729-741 (1996)
    • (1996) Numerical Methods Partial Diff. Eqs. , vol.12 , pp. 729-741
    • Lee, M.1    Milner, F.A.2
  • 32
    • 84968480755 scopus 로고
    • A mixed finite element method for a strongly nonlinear second order ellipticproblem
    • Milner, F.A., Park, E.J.: A mixed finite element method for a strongly nonlinear second order ellipticproblem. Math. Comput. 64, 973-988 (1995)
    • (1995) Math. Comput. , vol.64 , pp. 973-988
    • Milner, F.A.1    Park, E.J.2
  • 33
    • 0030486473 scopus 로고    scopus 로고
    • Mixed finite element methods for Hamilton-Jacobi-Bellman-type equations
    • Milner, F.A., Park, E.J.: Mixed finite element methods for Hamilton-Jacobi-Bellman-type equations. IMA J. Numerical Anal. 16, 399-412 (1996)
    • (1996) IMA J. Numerical Anal. , vol.16 , pp. 399-412
    • Milner, F.A.1    Park, E.J.2
  • 35
    • 17844375220 scopus 로고
    • Mathematical theory of elastic and elasto-plastic bodies: An introduction
    • Amsterdam Oxford New York: Elsevier Scientific Publishing Company
    • Necas, J., Hlavacek, I.: Mathematical theory of elastic and elasto-plastic bodies: An introduction. Studies in Applied Mechanics 3, Amsterdam Oxford New York: Elsevier Scientific Publishing Company 1981
    • (1981) Studies in Applied Mechanics , vol.3
    • Necas, J.1    Hlavacek, I.2
  • 37
    • 85030677729 scopus 로고
    • Mixed finite element methods for nonlinear second order elliptic problems
    • Park, E.J.: Mixed finite element methods for nonlinear second order elliptic problems. SIAM. J. Numerical Anal. 32, 865-885 (1995)
    • (1995) SIAM. J. Numerical Anal. , vol.32 , pp. 865-885
    • Park, E.J.1
  • 38
    • 34249971216 scopus 로고
    • A posteriori error estimators for the Stokes problem
    • Verfürth, R.: A posteriori error estimators for the Stokes problem. Numerische Mathematik 55, 309-325 (1989)
    • (1989) Numerische Mathematik , vol.55 , pp. 309-325
    • Verfürth, R.1
  • 39
    • 0003207769 scopus 로고    scopus 로고
    • A review of A-Posteriori error estimation and adaptive mesh-refinement techniques
    • John Wiley and Teubner Series
    • Verfürth, R.: A Review of A-Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques. John Wiley and Teubner Series. Advances in Numerical Mathematics 1996
    • (1996) Advances in Numerical Mathematics
    • Verfürth, R.1


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