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Volumn 41, Issue 5, 2003, Pages 1751-1772

Error estimates for low-order isoparametric quadrilateral finite elements for plates

Author keywords

Isoparametric quadrilaterals; MITC methods; Reissner Mindlin

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; CONVERGENCE OF NUMERICAL METHODS; FINITE ELEMENT METHOD; INTEGRATION; INTERPOLATION; MATHEMATICAL MODELS; PERTURBATION TECHNIQUES; TENSORS;

EID: 9244256739     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142902409410     Document Type: Conference Paper
Times cited : (41)

References (24)
  • 1
    • 0012757939 scopus 로고
    • A study of the free vibrations of square plates with various edge conditions
    • E. Hinton, ed., Pineridge Press, Swansea, UK
    • B. S. AL JANABI AND E. HINTON, A study of the free vibrations of square plates with various edge conditions, in Numerical Methods and Software for Dynamic Analysis of Plates and Shells, E. Hinton, ed., Pineridge Press, Swansea, UK, 1988, pp. 167-204.
    • (1988) Numerical Methods and Software for Dynamic Analysis of Plates and Shells , pp. 167-204
    • Janabi, B.S.A.L.1    Hinton, E.2
  • 2
    • 0001214001 scopus 로고
    • A uniformly accurate finite element method for the Reissner-Mindlin plate
    • D. N. ARNOLD AND R. S. FALK, A uniformly accurate finite element method for the Reissner-Mindlin plate, SIAM J. Numer. Anal., 26 (1989) pp. 1276-1290.
    • (1989) SIAM J. Numer. Anal. , vol.26 , pp. 1276-1290
    • Arnold, D.N.1    Falk, R.S.2
  • 3
    • 0036018011 scopus 로고    scopus 로고
    • Approximation by quadrilateral finite elements
    • D. N. ARNOLD, D. BOFFI, AND R. S. FALK, Approximation by quadrilateral finite elements, Math. Comp., 71 (2002), pp. 909-922.
    • (2002) Math. Comp. , vol.71 , pp. 909-922
    • Arnold, D.N.1    Boffi, D.2    Falk, R.S.3
  • 5
    • 54249116319 scopus 로고
    • Eigenvalue problems
    • P. G. Ciarlet and J. L. Lions, eds., North-Holland, Amsterdam
    • I. BABUŠKA AND J. OSBORN, Eigenvalue problems, in Handbook of Numerical Analysis, Vol. II, P. G. Ciarlet and J. L. Lions, eds., North-Holland, Amsterdam, 1991, pp. 641-787.
    • (1991) Handbook of Numerical Analysis , vol.2 , pp. 641-787
    • Babuška, I.1    Osborn, J.2
  • 6
    • 0022332230 scopus 로고
    • On the convergence of o four-node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation
    • J. R. Whiteman, ed., Academic Press, London
    • K.-J. BATHE AND F. BREZZI, On the convergence of o four-node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation, in The Mathematics of Finite Elements and Applications V, J. R. Whiteman, ed., Academic Press, London, 1985, pp. 491-503.
    • (1985) The Mathematics of Finite Elements and Applications V , pp. 491-503
    • Bathe, K.-J.1    Brezzi, F.2
  • 7
    • 0022010474 scopus 로고
    • A four-node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation
    • K.-J. BATHE AND E. N. DVORKIN, A four-node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation, Internat. J. Numer. Methods Engrg., 21 (1985), pp. 367-383.
    • (1985) Internat. J. Numer. Methods Engrg. , vol.21 , pp. 367-383
    • Bathe, K.-J.1    Dvorkin, E.N.2
  • 10
    • 0000083083 scopus 로고
    • Quasi-optimal error bounds for approximation of shear-stresses in Mindlin-Reissner plate models
    • F. BREZZI, M. FORTIN, AND R. STENBERG, Quasi-optimal error bounds for approximation of shear-stresses in Mindlin-Reissner plate models, Math. Models Methods Appl. Sci., 1 (1991), pp. 125-151.
    • (1991) Math. Models Methods Appl. Sci. , vol.1 , pp. 125-151
    • Brezzi, F.1    Fortin, M.2    Stenberg, R.3
  • 11
    • 8544220284 scopus 로고
    • Basic error estimates for elliptic problems
    • P. G. Ciarlet and J. L. Lions, eds., North-Holland, Amsterdam
    • P. G. CIARLET, Basic error estimates for elliptic problems, in Handbook of Numerical Analysis, Vol. II, P. G. Ciarlet and J. L. Lions, eds., North-Holland, Amsterdam, 1991, pp. 17-351.
    • (1991) Handbook of Numerical Analysis , vol.2 , pp. 17-351
    • Ciarlet, P.G.1
  • 12
    • 84968515343 scopus 로고
    • On mixed finite element methods for the Reissner-Mindlin plate model
    • R. DURÁN AND E. LIBERMAN, On mixed finite element methods for the Reissner-Mindlin plate model, Math. Comp., 58 (1992), pp. 561-573.
    • (1992) Math. Comp. , vol.58 , pp. 561-573
    • Durán, R.1    Liberman, E.2
  • 13
    • 0033443127 scopus 로고    scopus 로고
    • Approximation of the vibration modes of a plate by Reissner-Mindlin equations
    • R. DURÁN, L. HERVELLA-NIETO, E. LIBERMAN, R. RODRÍGUES, AND J. SOLOMIN, Approximation of the vibration modes of a plate by Reissner-Mindlin equations, Math. Comp., 68 (1999), pp. 1447-1463.
    • (1999) Math. Comp. , vol.68 , pp. 1447-1463
    • Durán, R.1    Hervella-Nieto, L.2    Liberman, E.3    Rodrígues, R.4    Solomin, J.5
  • 15
    • 0037402034 scopus 로고    scopus 로고
    • Computation of the vibration modes of plates and shells by low-order MITC quadrilateral finite elements
    • E. HERNÁNDEZ, L. HERVELLA-NIETO, AND R. RODRÍGUEZ, Computation of the vibration modes of plates and shells by low-order MITC quadrilateral finite elements, Comput. & Structures, 81 (2003), pp. 615-628.
    • (2003) Comput. & Structures , vol.81 , pp. 615-628
    • Hernández, E.1    Hervella-Nieto, L.2    Rodríguez, R.3
  • 18
    • 0039115258 scopus 로고
    • Uniform convergence of mixed interpolated elements for Reissner-Mindlin plates
    • P. PEISKER AND D. BRAESS, Uniform convergence of mixed interpolated elements for Reissner-Mindlin plates, M2AN Math. Model. Numer. Anal., 26 (1992), pp. 557-574.
    • (1992) M2AN Math. Model. Numer. Anal. , vol.26 , pp. 557-574
    • Peisker, P.1    Braess, D.2
  • 19
    • 0022314040 scopus 로고
    • Error bounds for the approximation of the Stokes problem using bilinear/constant elements on irregular quadrilateral meshes
    • J. R. Whiteman, ed., Academic Press, London
    • J. PITKÄRANTA AND R. STENBERG, Error bounds for the approximation of the Stokes problem using bilinear/constant elements on irregular quadrilateral meshes, in The Mathematics of Finite Elements and Applications V, J. R. Whiteman, ed., Academic Press, London, 1985, pp. 325-334.
    • (1985) The Mathematics of Finite Elements and Applications V , pp. 325-334
    • Pitkäranta, J.1    Stenberg, R.2
  • 20
    • 0040455245 scopus 로고    scopus 로고
    • Design principles and error analysis for reduced-shear plate-bending finite elements
    • J. PITKÄRANTA AND M. SURI, Design principles and error analysis for reduced-shear plate-bending finite elements, Numer. Math., 75 (1996), pp. 223-266.
    • (1996) Numer. Math. , vol.75 , pp. 223-266
    • Pitkäranta, J.1    Suri, M.2
  • 21
    • 0001175293 scopus 로고
    • A mixed finite element method for second order elliptic problems
    • Mathematical Aspects of Finite Element Methods, I. Galligani and E. Magenes, eds., Springer-Verlag, Berlin
    • P. A. RAVIART AND J. M. THOMAS, A mixed finite element method for second order elliptic problems, in Mathematical Aspects of Finite Element Methods, Lecture Notes in Mathematics 606, I. Galligani and E. Magenes, eds., Springer-Verlag, Berlin, 1977, pp. 292-315.
    • (1977) Lecture Notes in Mathematics , vol.606 , pp. 292-315
    • Raviart, P.A.1    Thomas, J.M.2
  • 22
    • 84968512389 scopus 로고
    • Analysis of mixed finite element methods for the Stokes problem: A unified approach
    • R. STENBERG, Analysis of mixed finite element methods for the Stokes problem: A unified approach, Math. Comp., 42 (1984), pp. 9-23.
    • (1984) Math. Comp. , vol.42 , pp. 9-23
    • Stenberg, R.1
  • 23
    • 0346879197 scopus 로고    scopus 로고
    • An hp error analysis of MITC plate elements
    • R. STENBERG AND M. SURI, An hp error analysis of MITC plate elements, SIAM J. Numer. Anal., 34 (1997), pp. 544-568.
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 544-568
    • Stenberg, R.1    Suri, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.