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Volumn 75, Issue 255, 2006, Pages 1087-1102

Locking-free adaptive discontinuous Galerkin FEM for linear elasticity problems

Author keywords

A posteriori error estimation; Adaptivity; Discontinuous Galerkin FEM; Linear elasticity; Locking

Indexed keywords


EID: 33746354292     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-06-01815-1     Document Type: Article
Times cited : (72)

References (26)
  • 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., 39:1749-1779, 2001. MR1885715 (2002k:65183)
    • (2001) SIAM J. Numer. Anal. , vol.39 , pp. 1749-1779
    • Arnold, D.N.1    Brezzi, F.2    Cockburn, B.3    Marini, L.D.4
  • 2
    • 0026940998 scopus 로고
    • On locking and robustness in the finite element method
    • MR1182731 (94c:65128)
    • I. Babuška and M. Suri. On locking and robustness in the finite element method. SIAM J. Numer. Anal., 29(5): 1261-1293, 1992. MR1182731 (94c:65128)
    • (1992) SIAM J. Numer. Anal. , vol.29 , Issue.5 , pp. 1261-1293
    • Babuška, I.1    Suri, M.2
  • 3
    • 84904152686 scopus 로고
    • Finite element methods for elliptic equations using nonconforming elements
    • MR0431742 (55:4737)
    • G. A. Baker. Finite element methods for elliptic equations using nonconforming elements. Math. Comp., 31:45-59, 1977. MR0431742 (55:4737)
    • (1977) Math. Comp. , vol.31 , pp. 45-59
    • Baker, G.A.1
  • 4
    • 0037474430 scopus 로고    scopus 로고
    • Energy norm a posteriori error estimation for discontinuous Galerkin methods
    • MR1952357 (2003k:65135)
    • R. Becker, P. Hansbo, and M.G. Larson. Energy norm a posteriori error estimation for discontinuous Galerkin methods. Comput. Methods Appl. Mech. Engrg., 192:723-733, 2003. MR1952357 (2003k:65135)
    • (2003) Comput. Methods Appl. Mech. Engrg. , vol.192 , pp. 723-733
    • Becker, R.1    Hansbo, P.2    Larson, M.G.3
  • 5
    • 2942670777 scopus 로고    scopus 로고
    • 1 vector fields
    • MR2047078 (2005c:65096)
    • 1 vector fields. Math. Comp., 73(247):1067-1087, 2004. MR2047078 (2005c:65096)
    • (2004) Math. Comp. , vol.73 , Issue.247 , pp. 1067-1087
    • Brenner, S.C.1
  • 7
    • 84968487611 scopus 로고
    • Linear finite element methods for planar linear elasticity
    • MR1140646 (93a:73078)
    • S. C. Brenner and L. Sung. Linear finite element methods for planar linear elasticity. Math. Comp., 59:321-338, 1992. MR1140646 (93a:73078)
    • (1992) Math. Comp. , vol.59 , pp. 321-338
    • Brenner, S.C.1    Sung, L.2
  • 9
    • 0035930913 scopus 로고    scopus 로고
    • Averaging technique for a posteriori error control in elasticity. Part III: Locking-free nonconforming FEM
    • MR1870519 (2002j:65106)
    • C. Carstensen and S. A. Funken. Averaging technique for a posteriori error control in elasticity. Part III: Locking-free nonconforming FEM. Comput. Methods Appl. Mech. Engrg., 191:861-877, 2001. MR1870519 (2002j:65106)
    • (2001) Comput. Methods Appl. Mech. Engrg. , vol.191 , pp. 861-877
    • Carstensen, C.1    Funken, S.A.2
  • 10
    • 0002559725 scopus 로고    scopus 로고
    • Locking-free mixed stabilized finite element methods for bending-dominated shells
    • Amer. Math. Soc. MR1696529 (2000e:74099)
    • D. Chapelle and R. Stenberg. Locking-free mixed stabilized finite element methods for bending-dominated shells. In Plates and shells, CRM Proc. Lecture Notes, volume 21, pages 81-94. Amer. Math. Soc., 1999. MR1696529 (2000e:74099)
    • (1999) Plates and Shells, CRM Proc. Lecture Notes , vol.21 , pp. 81-94
    • Chapelle, D.1    Stenberg, R.2
  • 11
    • 0001456343 scopus 로고
    • Interior penalty procedures for elliptic and parabolic Galerkin methods
    • Springer-Verlag, Berlin. MR0440955 (55:13823)
    • J. Douglas Jr. and T. Dupont. Interior penalty procedures for elliptic and parabolic Galerkin methods. In Lecture Notes in Phys. 58. Springer-Verlag, Berlin, 1976. MR0440955 (55:13823)
    • (1976) Lecture Notes in Phys. , vol.58
    • Douglas Jr., J.1    Dupont, T.2
  • 12
    • 0037085994 scopus 로고    scopus 로고
    • Discontinuous Galerkin methods for incompressible and nearly incompressible elasticity by Nitsche's method
    • MR1886000 (2003j:74057)
    • P. Hansbo and M. G. Larson. Discontinuous Galerkin methods for incompressible and nearly incompressible elasticity by Nitsche's method. Comput. Methods Appl. Mech. Engrg., 191(17-18):1895-1908, 2002. MR1886000 (2003j:74057)
    • (2002) Comput. Methods Appl. Mech. Engrg. , vol.191 , Issue.17-18 , pp. 1895-1908
    • Hansbo, P.1    Larson, M.G.2
  • 13
    • 20144385612 scopus 로고    scopus 로고
    • Mixed discontinuous Galerkin approximation of the Maxwell operator
    • MR2051073 (2005b:65128)
    • P. Houston, I. Perugia, and D. Schötzau. Mixed discontinuous Galerkin approximation of the Maxwell operator. SIAM J. Numer. Anal., 42(1):434-459, 2003. MR2051073 (2005b:65128)
    • (2003) SIAM J. Numer. Anal. , vol.42 , Issue.1 , pp. 434-459
    • Houston, P.1    Perugia, I.2    Schötzau, D.3
  • 14
    • 10444236497 scopus 로고    scopus 로고
    • Energy norm a posteriori error estimation for mixed discontinuous Galerkin approximations of the Maxwell operator
    • MR2105178 (2005h:78027)
    • P. Houston, I. Perugia, and D. Schötzau. Energy norm a posteriori error estimation for mixed discontinuous Galerkin approximations of the Maxwell operator. Comput. Methods Appl. Mech. Engrg., 194(2-5):499-510, 2005. MR2105178 (2005h:78027)
    • (2005) Comput. Methods Appl. Mech. Engrg. , vol.194 , Issue.2-5 , pp. 499-510
    • Houston, P.1    Perugia, I.2    Schötzau, D.3
  • 15
    • 17444413054 scopus 로고    scopus 로고
    • Energy norm a posteriori error estimation for mixed discontinuous Galerkin approximations of the Stokes problem
    • MR2142201
    • P. Houston, D. Schötzau, and T. P. Wihler. Energy norm a posteriori error estimation for mixed discontinuous Galerkin approximations of the Stokes problem. J. Sci. Comput., 22/23:347-370, 2005. MR2142201
    • (2005) J. Sci. Comput. , vol.22-23 , pp. 347-370
    • Houston, P.1    Schötzau, D.2    Wihler, T.P.3
  • 16
    • 33645914154 scopus 로고    scopus 로고
    • An hp-adaptive mixed discontinuous Galerkin FEM for nearly incompressible linear elasticity
    • to appear
    • P. Houston, D. Schötzau, and T. P. Wihler. An hp-adaptive mixed discontinuous Galerkin FEM for nearly incompressible linear elasticity. Comput. Methods Appl. Mech. Engrg. (to appear).
    • Comput. Methods Appl. Mech. Engrg.
    • Houston, P.1    Schötzau, D.2    Wihler, T.P.3
  • 17
    • 11044220115 scopus 로고    scopus 로고
    • A posteriori error estimates for a discontinuous Galerkin approximation of second-order elliptic problems
    • MR2034620 (2005d:65192)
    • O.A. Karakashian and F. Pascal. A posteriori error estimates for a discontinuous Galerkin approximation of second-order elliptic problems. SIAM J. Numer. Anal., 41(6):2374-2399, 2003. MR2034620 (2005d:65192)
    • (2003) SIAM J. Numer. Anal. , vol.41 , Issue.6 , pp. 2374-2399
    • Karakashian, O.A.1    Pascal, F.2
  • 18
    • 0029328850 scopus 로고
    • A linear nonconforming finite element method for nearly incompressible elasticity and Stokes flow
    • MR1343077 (96d:73073)
    • R. Kouhia and R. Stenberg. A linear nonconforming finite element method for nearly incompressible elasticity and Stokes flow. Comput. Methods Appl. Mech. Engrg., 124(3):195-212, 1995. MR1343077 (96d:73073)
    • (1995) Comput. Methods Appl. Mech. Engrg. , vol.124 , Issue.3 , pp. 195-212
    • Kouhia, R.1    Stenberg, R.2
  • 20
    • 0348152044 scopus 로고    scopus 로고
    • An hp-analysis of the local discontinuous Galerkin method for diffusion problems
    • MR1910752
    • I. Perugia and D. Schötzau. An hp-analysis of the local discontinuous Galerkin method for diffusion problems. J. Sci. Comput., 17:561-571, 2002. MR1910752
    • (2002) J. Sci. Comput. , vol.17 , pp. 561-571
    • Perugia, I.1    Schötzau, D.2
  • 21
    • 0041823208 scopus 로고    scopus 로고
    • A posteriori error estimates for a discontinuous Galerkin method applied to elliptic problems
    • MR2015276 (2004j:65169)
    • B. Rivière and M. F. Wheeler. A posteriori error estimates for a discontinuous Galerkin method applied to elliptic problems. Comput. Math. Appl., 46(1):141-163, 2003. MR2015276 (2004j:65169)
    • (2003) Comput. Math. Appl. , vol.46 , Issue.1 , pp. 141-163
    • Rivière, B.1    Wheeler, M.F.2
  • 22
    • 0345708744 scopus 로고    scopus 로고
    • Mixed hp-DGFEM for incompressible flows
    • MR1974180 (2004k:65161)
    • D. Schötzau, C. Schwab, and A. Toselli. Mixed hp-DGFEM for incompressible flows. SIAM J. Numer. Anal., 40:2171-2194, 2003. MR1974180 (2004k:65161)
    • (2003) SIAM J. Numer. Anal. , vol.40 , pp. 2171-2194
    • Schötzau, D.1    Schwab, C.2    Toselli, A.3
  • 24
    • 34250154462 scopus 로고
    • An analysis of the p-version of the finite element method for nearly incompressible materials
    • MR0696549 (85f:65113b)
    • M. Vogelius. An analysis of the p-version of the finite element method for nearly incompressible materials. Numer. Math., 41:39-53, 1983. MR0696549 (85f:65113b)
    • (1983) Numer. Math. , vol.41 , pp. 39-53
    • Vogelius, M.1
  • 25
    • 0000802762 scopus 로고
    • An elliptic collocation finite element method with interior penalties
    • MR0471383 (57:11117)
    • M. F. Wheeler. An elliptic collocation finite element method with interior penalties. SIAM J. Numer. Anal., 15:152-161, 1978. MR0471383 (57:11117)
    • (1978) SIAM J. Numer. Anal. , vol.15 , pp. 152-161
    • Wheeler, M.F.1
  • 26
    • 1642499378 scopus 로고    scopus 로고
    • Locking-free DGFEM for elasticity problems in polygons
    • MR2027288 (2004i:74108)
    • T. P. Wihler. Locking-free DGFEM for elasticity problems in polygons. IMA J. Numer. Anal., 24(1):45-75, 2004. MR2027288 (2004i:74108)
    • (2004) IMA J. Numer. Anal. , vol.24 , Issue.1 , pp. 45-75
    • Wihler, T.P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.