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Mathematics of Computation
Volumn 76, Issue 260, 2007, Pages 1771-1786
Two lower order nonconforming rectangular elements for the reissner-mindlin plate
Author keywords

Bilinear element; Bubble function; Locking free; Reissner Mindlin plate; Rotated Q1 element
Indexed keywords

EID: 38849101528     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-07-01952-7     Document Type: Article
Times cited : (11)
References (28)
  • 1
    • 0036410391 scopus 로고    scopus 로고
    • Unified analysis of discontinuous Galerkin methods for elliptic problems
    • MR1885715 2002k:65183
    • D.N. ARNOLD, F. BREZZI, B. COCKBURN AND L.D. MARINI, Unified analysis of discontinuous Galerkin methods for elliptic problems, SIAM. J. Numer. Anal., 2002 (39), pp. 1749-1779. MR1885715 (2002k:65183)
    • (2002) SIAM. J. Numer. Anal , vol.39 , pp. 1749-1779
    • ARNOLD, D.N.1    BREZZI, F.2    COCKBURN, B.3    MARINI, L.D.4
  • 2
    • 17444422862 scopus 로고    scopus 로고
    • A family of discontinuous Galerkin finite elements for Reissner-Mindlin plate
    • MR2142189 2006b:65160
    • D.N. ARNOLD, F. BREZZI AND L.D. MARINI, A family of discontinuous Galerkin finite elements for Reissner-Mindlin plate, J. Sci. Comp., 2005 (22), pp. 25-41. MR2142189 (2006b:65160)
    • (2005) J. Sci. Comp , vol.22 , pp. 25-41
    • ARNOLD, D.N.1    BREZZI, F.2    MARINI, L.D.3
  • 3
    • 0001214001 scopus 로고
    • A uniformly accurate finite element method for Reissner-Mindlin plates
    • MR1025088 91c:65068
    • D.N. ARNOLD AND R.S. FALK, A uniformly accurate finite element method for Reissner-Mindlin plates, SIAM. J. Numer. Anal., 1989 (28), pp. 1276-1290. MR1025088 (91c:65068)
    • (1989) SIAM. J. Numer. Anal , vol.28 , pp. 1276-1290
    • ARNOLD, D.N.1    FALK, R.S.2
  • 4
    • 84966254458 scopus 로고
    • Numerical approximation of Reissner-Mindlin plates
    • MR842127 87g:73057
    • K. J. BATHE, F. BREZZI AND M. FORTIN, Numerical approximation of Reissner-Mindlin plates, Math Comp., 1986 (47), pp. 151-158. MR842127 (87g:73057)
    • (1986) Math Comp , vol.47 , pp. 151-158
    • BATHE, K.J.1    BREZZI, F.2    FORTIN, M.3
  • 5
    • 0024715444 scopus 로고
    • Mixed-interpolated elements for Reissner-Mindlin plates
    • MR1008138 90g:73090
    • K. J. BATHE, F. BREZZI AND M. FORTIN, Mixed-interpolated elements for Reissner-Mindlin plates, Int. J. Num. Meths. Engreg., 1989 (28), pp. 1787-1801. MR1008138 (90g:73090)
    • (1989) Int. J. Num. Meths. Engreg , vol.28 , pp. 1787-1801
    • BATHE, K.J.1    BREZZI, F.2    FORTIN, M.3
  • 7
    • 1842459324 scopus 로고    scopus 로고
    • 1 functions
    • MR1974504 2004d:65140
    • 1 functions, SIAM. J. Numer, Anal., 2003 (41), pp. 306-324. MR1974504 (2004d:65140)
    • (2003) SIAM. J. Numer, Anal , vol.41 , pp. 306-324
    • BRENNER, S.C.1
  • 8
    • 2942670777 scopus 로고    scopus 로고
    • 1 vector fields
    • MR2047078 2005c:65096
    • 1 vector fields, Math.Comp., 2004 (73), pp. 1067-1087. MR2047078 (2005c:65096)
    • (2004) Math.Comp , vol.73 , pp. 1067-1087
    • BRENNER, S.C.1
  • 10
    • 0000083083 scopus 로고
    • Error analysis of mixed-interpolated elements for Reissner-Mindlin plate
    • MR1115287 92e:73030
    • F. BREZZI, M. FORTIN AND R. STENBERG, Error analysis of mixed-interpolated elements for Reissner-Mindlin plate, Math. Models. Meth. Appl. Sci., 1991 (1), pp. 125-151. MR1115287 (92e:73030)
    • (1991) Math. Models. Meth. Appl. Sci , vol.1 , pp. 125-151
    • BREZZI, F.1    FORTIN, M.2    STENBERG, R.3
  • 11
    • 0037401609 scopus 로고    scopus 로고
    • A nonconforming element for Reissner-Mindlin plate
    • MR2001877 2005f:74074
    • F. BREZZI AND L.D. MARINI, A nonconforming element for Reissner-Mindlin plate, Computers & Structures, 2003 (81), pp. 515-522. MR2001877 (2005f:74074)
    • (2003) Computers & Structures , vol.81 , pp. 515-522
    • BREZZI, F.1    MARINI, L.D.2
  • 12
    • 38849135098 scopus 로고    scopus 로고
    • P.G. CIARLET, The Finite Element Method for Elliptic Problems. North-Holland, 1978; reprinted as SIAM Classics in Applied Mathematics, 2002. MR0520174 (58:25001)
    • P.G. CIARLET, The Finite Element Method for Elliptic Problems. North-Holland, 1978; reprinted as SIAM Classics in Applied Mathematics, 2002. MR0520174 (58:25001)
  • 13
    • 0043139650 scopus 로고
    • Nonconforming elements in the mixed finite element method
    • MR815417 87d:65130
    • HOU DE HAN, Nonconforming elements in the mixed finite element method, J. Comp. Math., 1984 (2), pp. 223-233. MR815417 (87d:65130)
    • (1984) J. Comp. Math , vol.2 , pp. 223-233
    • HOU, D.H.1
  • 14
    • 38849194921 scopus 로고    scopus 로고
    • 1 element for Reissner-Mindlin plate, J. Comp. Math., 2003 (21), pp. 25-32. R1974269 (2004c:65143)
    • 1 element for Reissner-Mindlin plate, J. Comp. Math., 2003 (21), pp. 25-32. R1974269 (2004c:65143)
  • 15
    • 11444257287 scopus 로고    scopus 로고
    • On the superconvergence of nonconforming low order finite elements applied to the Poisson equation
    • MR2110239 2005k:65256
    • Q. LIN, L. TOBISKA AND A. ZHOU, On the superconvergence of nonconforming low order finite elements applied to the Poisson equation, IMA. J. Numer.Anal., 2005(25), pp. 160-181. MR2110239 (2005k:65256)
    • (2005) IMA. J. Numer.Anal , vol.25 , pp. 160-181
    • LIN, Q.1    TOBISKA, L.2    ZHOU, A.3
  • 16
    • 27344450256 scopus 로고    scopus 로고
    • A lower-order nonconforming finite element for Reissner-Mindlin plates
    • MR2139411 2006b:65172
    • C. LOVADINA, A lower-order nonconforming finite element for Reissner-Mindlin plates, SIAM. J. Numer. Anal., 2005 (42),pp. 2688-2705 . MR2139411 (2006b:65172)
    • (2005) SIAM. J. Numer. Anal , vol.42 , pp. 2688-2705
    • LOVADINA, C.1
  • 18
    • 25144483302 scopus 로고    scopus 로고
    • TWO nonconforming quadrilateral finite elements for Reissner-Mindlin plate
    • MR2168943 2006g:74103
    • PINGBING MING AND ZHONG-CI SHI, TWO nonconforming quadrilateral finite elements for Reissner-Mindlin plate, Math. Model. Meth. Appl. Sci., 2005 (15), pp. 1503-1518. MR2168943 (2006g:74103)
    • (2005) Math. Model. Meth. Appl. Sci , vol.15 , pp. 1503-1518
    • PINGBING, M.I.N.G.1    ZHONG-CI, S.H.I.2
  • 19
    • 0039115258 scopus 로고
    • Uniform convergence of mixed interpolated elements for Reissner-Mindlin plates
    • MR1177387 93j:73070
    • P. PEISKER and D. BRAESS, Uniform convergence of mixed interpolated elements for Reissner-Mindlin plates, RAIRO. Anal. Numér., 1992 (26), pp. 557-574. MR1177387 (93j:73070)
    • (1992) RAIRO. Anal. Numér , vol.26 , pp. 557-574
    • PEISKER, P.1    BRAESS, D.2
  • 20
    • 0001506556 scopus 로고
    • Analysis of some low-order finite element schemes for Mindlin-Reissner and Kirchhoff plates
    • MR946378 89f:65126
    • J. PITKÄRANTA, Analysis of some low-order finite element schemes for Mindlin-Reissner and Kirchhoff plates, Numer. Math., 1988 (53), pp. 237-254. MR946378 (89f:65126)
    • (1988) Numer. Math , vol.53 , pp. 237-254
    • PITKÄRANTA, J.1
  • 21
    • 0040455245 scopus 로고    scopus 로고
    • Design principles and error analysis for reduced-shear plate bending finite elements
    • MR1421988 98c:73078
    • J. PITKÄRANTA AND M. SURI Design principles and error analysis for reduced-shear plate bending finite elements, Numer. Math., 1996 (75), pp. 223-266. MR1421988 (98c:73078)
    • (1996) Numer. Math , vol.75 , pp. 223-266
    • PITKÄRANTA, J.1    SURI, M.2
  • 22
    • 0026837268 scopus 로고
    • Simple nonconforming quadrilateral Stokes element
    • MR1148797 92i:65170
    • R. RANNARCHER AND S. TUREK, Simple nonconforming quadrilateral Stokes element, Numer. Meth. Part. Diff. Equations., 1992 (8), pp. 97-111. MR1148797 (92i:65170)
    • (1992) Numer. Meth. Part. Diff. Equations , vol.8 , pp. 97-111
    • RANNARCHER, R.1    TUREK, S.2
  • 23
    • 84966200902 scopus 로고
    • Finite element interpolation of nonsmooth functions satisfying boundary conditions
    • MR1011446 90j:65021
    • L. R. SCOTT AND S. ZHANG, Finite element interpolation of nonsmooth functions satisfying boundary conditions, Math. Comp., 1990 (54), pp. 483-493. MR1011446 (90j:65021)
    • (1990) Math. Comp , vol.54 , pp. 483-493
    • SCOTT, L.R.1    ZHANG, S.2
  • 24
    • 0000919652 scopus 로고
    • A convergence condition for quadrilateral Wilson element
    • MR757491 86d:65151
    • ZHONG-CI SHI, A convergence condition for quadrilateral Wilson element, Numer. Math., 1984 (44), pp. 349-361. MR757491 (86d:65151)
    • (1984) Numer. Math , vol.44 , pp. 349-361
    • ZHONG-CI, S.H.I.1
  • 25
    • 84966218182 scopus 로고
    • The F-E-M-Test for nonconforming finite elements
    • MR906178 88g:65120
    • ZHONG-CI SHI, The F-E-M-Test for nonconforming finite elements, Mathematics of Computation, 1987 (49), pp. 391-405. MR906178 (88g:65120)
    • (1987) Mathematics of Computation , vol.49 , pp. 391-405
    • ZHONG-CI, S.H.I.1
  • 26
    • 84968512389 scopus 로고
    • Analysis of mixed finite element methods for the stokes problems: A unified approach
    • MR0725982 84k:76014
    • R. STENBERG , Analysis of mixed finite element methods for the stokes problems: A unified approach, Math. Comp., 1984 (42), pp. 9-23. MR0725982 (84k:76014)
    • (1984) Math. Comp , vol.42 , pp. 9-23
    • STENBERG, R.1
  • 27
    • 84968504247 scopus 로고
    • Locking effects in the finite element approximation of plate models
    • MR1277772 95f:65207
    • M. SURI, I. BABUŠKA AND C. SCHWAB, Locking effects in the finite element approximation of plate models, Math. Comp., 1995 (64), pp. 461-482. MR1277772 (95f:65207)
    • (1995) Math. Comp , vol.64 , pp. 461-482
    • SURI, M.1    BABUŠKA, I.2    SCHWAB, C.3
  • 28
    • 0005381023 scopus 로고    scopus 로고
    • XIU YE, A rectangular element for the Reissner-Mindlin plate, Numer. Meth. Part. Diff. Equations, 2000. MR1740136 (2000j:74093)
    • XIU YE, A rectangular element for the Reissner-Mindlin plate, Numer. Meth. Part. Diff. Equations, 2000. MR1740136 (2000j:74093)

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