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Volumn 42, Issue 2, 2004, Pages 826-842

Least-squares methods for linear elasticity

Author keywords

Incompressible limit; Least squares method; Linear elasticity; Mixed finite element method

Indexed keywords

DISPLACEMENT; INCOMPRESSIBLE LIMIT; LINEAR ELASTICITY; STRESS TENSORS;

EID: 10144254912     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142902418357     Document Type: Article
Times cited : (109)

References (23)
  • 1
    • 34250136581 scopus 로고
    • A family of higher order mixed finite element methods for plane elasticity
    • D. N. ARNOLD, J. DOUGLAS, AND C. P. GUPTA, A family of higher order mixed finite element methods for plane elasticity, Numer. Math., 45 (1984), pp. 1-22.
    • (1984) Numer. Math. , vol.45 , pp. 1-22
    • Arnold, D.N.1    Douglas, J.2    Gupta, C.P.3
  • 2
    • 0034386185 scopus 로고    scopus 로고
    • Multigrid in H(div) and H (curl)
    • D. N. ARNOLD, R. S. FALK, AND R. WINTHER, Multigrid in H(div) and H (curl), Numer. Math., 85 (2000), pp. 197-217.
    • (2000) Numer. Math. , vol.85 , pp. 197-217
    • Arnold, D.N.1    Falk, R.S.2    Winther, R.3
  • 3
    • 0036768154 scopus 로고    scopus 로고
    • Mixed finite elements for elasticity
    • D. N. ARNOLD AND R. WINTHER, Mixed finite elements for elasticity, Numer. Math., 42 (2002), pp. 401-419.
    • (2002) Numer. Math. , vol.42 , pp. 401-419
    • Arnold, D.N.1    Winther, R.2
  • 5
    • 0042041100 scopus 로고    scopus 로고
    • Local error estimates and adaptive refinement for first-order system least squares
    • M. BERNDT, T. A. MANTEUFFEL, AND S. F. MCCORMICK, Local error estimates and adaptive refinement for first-order system least squares, Electron. Trans. Numer. Anal., 6 (1997), pp. 35-43.
    • (1997) Electron. Trans. Numer. Anal. , vol.6 , pp. 35-43
    • Berndt, M.1    Manteuffel, T.A.2    Mccormick, S.F.3
  • 6
    • 0032294378 scopus 로고    scopus 로고
    • Finite element methods of least-squares type
    • P. B. BOCHEV AND M. D. GUNZBURGER, Finite element methods of least-squares type, SIAM Rev., 40 (1998), pp. 789-837.
    • (1998) SIAM Rev. , vol.40 , pp. 789-837
    • Bochev, P.B.1    Gunzburger, M.D.2
  • 7
    • 0031518552 scopus 로고    scopus 로고
    • A least-squares approach based on a discrete minus one inner product for first order systems
    • J. H. BRAMBLE, R. D. LAZAROV, AND J. E. PASCIAK, A least-squares approach based on a discrete minus one inner product for first order systems, Math. Comp., 66 (1997), pp. 935-955.
    • (1997) Math. Comp. , vol.66 , pp. 935-955
    • Bramble, J.H.1    Lazarov, R.D.2    Pasciak, J.E.3
  • 10
    • 18444403060 scopus 로고    scopus 로고
    • A least squares mixed finite element method for the stress-displacement formulation of linear elasticity: Error estimation and adaptive refinement
    • to appear
    • Z. CAI, J. KORSAWE, AND G. STARKE, A least squares mixed finite element method for the stress-displacement formulation of linear elasticity: Error estimation and adaptive refinement, Numer. Methods Partial Differential Equations, to appear.
    • Numer. Methods Partial Differential Equations
    • Cai, Z.1    Korsawe, J.2    Starke, G.3
  • 11
    • 0000441907 scopus 로고    scopus 로고
    • First-order system least squares (FOSLS) for planar linear elasticity: Pure traction problem
    • Z. CAI, T. A. MANTEUFFEL, S. F. MCCORMICK, AND S. V. PARTER, First-order system least squares (FOSLS) for planar linear elasticity: Pure traction problem, SIAM J. Numer. Anal., 35 (1998), pp. 320-335.
    • (1998) SIAM J. Numer. Anal. , vol.35 , pp. 320-335
    • Cai, Z.1    Manteuffel, T.A.2    Mccormick, S.F.3    Parter, S.V.4
  • 12
    • 2342588708 scopus 로고    scopus 로고
    • First-order system least squares for the stress-displacement formulation: Linear elasticity
    • Z. CAI AND G. STARKE, First-order system least squares for the stress-displacement formulation: Linear elasticity, SIAM J. Numer. Anal., 41 (2003), pp. 715-730.
    • (2003) SIAM J. Numer. Anal. , vol.41 , pp. 715-730
    • Cai, Z.1    Starke, G.2
  • 17
    • 0000626839 scopus 로고    scopus 로고
    • Multigrid method for Maxwell's equations
    • R. HIPTMAIR, Multigrid method for Maxwell's equations, SIAM J. Numer. Anal., 36 (1998), pp. 204-225.
    • (1998) SIAM J. Numer. Anal. , vol.36 , pp. 204-225
    • Hiptmair, R.1
  • 19
    • 0037196220 scopus 로고    scopus 로고
    • The least-squares finite element method in elasticity-Part I: Plane stress or strain with drilling degrees of freedom
    • B. JIANG AND J. WU, The least-squares finite element method in elasticity-Part I: Plane stress or strain with drilling degrees of freedom, Internat. J. Numer. Methods Engrg., 53 (2002), pp. 621-636.
    • (2002) Internat. J. Numer. Methods Engrg. , vol.53 , pp. 621-636
    • Jiang, B.1    Wu, J.2
  • 20
    • 0001175293 scopus 로고
    • A mixed finite element method for 2-nd order elliptic problems
    • in Mathematical Aspects of Finite Element Methods, I. Galligani and E. Magenes, eds., Springer-Verlag, New York
    • P.-A. RAVIART AND J.-M. THOMAS, A mixed finite element method for 2-nd order elliptic problems, in Mathematical Aspects of Finite Element Methods, Lecture Notes in Math. 606, I. Galligani and E. Magenes, eds., Springer-Verlag, New York, 1977, pp. 292-315.
    • (1977) Lecture Notes in Math. , vol.606 , pp. 292-315
    • Raviart, P.-A.1    Thomas, J.-M.2
  • 21
    • 0042233269 scopus 로고    scopus 로고
    • Multilevel boundary functional for least-squares mixed finite element methods
    • G. STARKE, Multilevel boundary functional for least-squares mixed finite element methods, SIAM J. Numer. Anal., 36 (1999), pp. 1065-1077.
    • (1999) SIAM J. Numer. Anal. , vol.36 , pp. 1065-1077
    • Starke, G.1
  • 23
    • 21144466078 scopus 로고
    • Multilevel iterative methods for mixed finite element discretizations of elliptic problems
    • P. S. VASSILEVSKI AND J. WANG, Multilevel iterative methods for mixed finite element discretizations of elliptic problems, Numer. Math., 63 (1992), pp. 503-520.
    • (1992) Numer. Math. , vol.63 , pp. 503-520
    • Vassilevski, P.S.1    Wang, J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.