메뉴 건너뛰기




Volumn 72, Issue 3, 2007, Pages 253-294

Diamond elements: A finite element/discrete-mechanics approximation scheme with guaranteed optimal convergence in incompressible elasticity

Author keywords

Discrete mechanics; Incompressible elasticity; Inf sup condition; Macroelements

Indexed keywords

BOUNDARY VALUE PROBLEMS; ELASTICITY; FINITE ELEMENT METHOD; INTERPOLATION; TOPOLOGY; TRIANGULATION;

EID: 35248861606     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.1992     Document Type: Article
Times cited : (34)

References (47)
  • 2
    • 34250459417 scopus 로고
    • The finite-element method with Lagrangian multipliers
    • Babuška I. The finite-element method with Lagrangian multipliers. Numerische Mathematik 1973; 20:179-182.
    • (1973) Numerische Mathematik , vol.20 , pp. 179-182
    • Babuška, I.1
  • 3
    • 0016093926 scopus 로고
    • On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers
    • Brezzi F. On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers. RAIRO Analyse Numérique, Série Rouge 1974; 8:129-151.
    • (1974) RAIRO Analyse Numérique, Série Rouge , vol.8 , pp. 129-151
    • Brezzi, F.1
  • 4
    • 0015762231 scopus 로고
    • Conforming and nonconforming finite element methods for solving the stationary Stokes equation
    • Crouzeix M, Raviart P-A. Conforming and nonconforming finite element methods for solving the stationary Stokes equation. RAIRO 1973; 3:33-75.
    • (1973) RAIRO , vol.3 , pp. 33-75
    • Crouzeix, M.1    Raviart, P.-A.2
  • 5
    • 0003385001 scopus 로고
    • Error estimates for finite element solution of the Stokes problem in the primitive variables
    • Bercovier M, Pironneau O. Error estimates for finite element solution of the Stokes problem in the primitive variables. Numerische Mathematik 1979; 33:211-224.
    • (1979) Numerische Mathematik , vol.33 , pp. 211-224
    • Bercovier, M.1    Pironneau, O.2
  • 6
    • 0002682177 scopus 로고
    • Error estimate for a mixed finite element approximation of the Stokes equation
    • Verfürth R. Error estimate for a mixed finite element approximation of the Stokes equation. RAIRO Analyse Numérique 1984; 18(2):175-182.
    • (1984) RAIRO Analyse Numérique , vol.18 , Issue.2 , pp. 175-182
    • Verfürth, R.1
  • 7
    • 51249186403 scopus 로고
    • A stable finite element for the Stokes equations
    • Arnold DN, Brezzi F, Fortin M. A stable finite element for the Stokes equations. Calcolo 1984; 21:337-344.
    • (1984) Calcolo , vol.21 , pp. 337-344
    • Arnold, D.N.1    Brezzi, F.2    Fortin, M.3
  • 8
    • 0019057349 scopus 로고
    • Generalization of selective integration procedures to anisotropic and nonlinear media
    • Hughes TJR. Generalization of selective integration procedures to anisotropic and nonlinear media. International Journal for Numerical Methods in Engineering 1980; 15:1413-1418.
    • (1980) International Journal for Numerical Methods in Engineering , vol.15 , pp. 1413-1418
    • Hughes, T.J.R.1
  • 10
    • 0842281995 scopus 로고    scopus 로고
    • Uniform convergence and a posteriori error estimators for the enhanced strain finite element method
    • Braess D, Carstensen C, Reddy BD. Uniform convergence and a posteriori error estimators for the enhanced strain finite element method. Numerische Mathematik 2004; 96:461-479.
    • (2004) Numerische Mathematik , vol.96 , pp. 461-479
    • Braess, D.1    Carstensen, C.2    Reddy, B.D.3
  • 11
    • 33751250393 scopus 로고    scopus 로고
    • Convergence in the incompressible limit of finite element approximations based on the Hu-Washizu formulation
    • Technical Report 2004-05, Stuttgart University
    • Lamichhane B, Reddy D, Wohlmuth B. Convergence in the incompressible limit of finite element approximations based on the Hu-Washizu formulation. Technical Report 2004-05, Stuttgart University, 2004.
    • (2004)
    • Lamichhane, B.1    Reddy, D.2    Wohlmuth, B.3
  • 12
    • 84966256275 scopus 로고
    • Error analysis of some finite element methods for the Stokes problem
    • Stenberg R. Error analysis of some finite element methods for the Stokes problem. Mathematics of Computation 1990; 54:495-508.
    • (1990) Mathematics of Computation , vol.54 , pp. 495-508
    • Stenberg, R.1
  • 14
    • 11244324581 scopus 로고    scopus 로고
    • Theory and Practice of Finite Elements
    • Springer: New York
    • Ern A, Guermond J-L. Theory and Practice of Finite Elements. Applied Mathematical Series, vol. 159. Springer: New York, 2004.
    • (2004) Applied Mathematical Series , vol.159
    • Ern, A.1    Guermond, J.-L.2
  • 17
    • 0347374101 scopus 로고
    • A conforming finite element method for two-dimensional incompressible elasticity
    • Mercier B. A conforming finite element method for two-dimensional incompressible elasticity. International Journal for Numerical Methods in Engineering 1979; 14:942-945.
    • (1979) International Journal for Numerical Methods in Engineering , vol.14 , pp. 942-945
    • Mercier, B.1
  • 19
    • 0019584612 scopus 로고
    • Compatibility condition and existence results in discrete finite incompressible elasticity
    • Le Tallec P. Compatibility condition and existence results in discrete finite incompressible elasticity. Computer Methods in Applied Mechanics and Engineering 1981; 27:239-259.
    • (1981) Computer Methods in Applied Mechanics and Engineering , vol.27 , pp. 239-259
    • Le Tallec, P.1
  • 20
    • 0001023383 scopus 로고
    • Stability of finite elements under divergence constraint
    • Boland J, Nicolaides RA. Stability of finite elements under divergence constraint. SIAM Journal on Numerical Analysis 1983; 20(4):722-731.
    • (1983) SIAM Journal on Numerical Analysis , vol.20 , Issue.4 , pp. 722-731
    • Boland, J.1    Nicolaides, R.A.2
  • 21
    • 0022075675 scopus 로고
    • Stable and semistable low order finite elements for viscous flows
    • Boland J, Nicolaides RA. Stable and semistable low order finite elements for viscous flows. SIAM Journal on Numerical Analysis 1985; 22:474-492.
    • (1985) SIAM Journal on Numerical Analysis , vol.22 , pp. 474-492
    • Boland, J.1    Nicolaides, R.A.2
  • 22
    • 84968512389 scopus 로고
    • Analysis of mixed finite element methods for the Stokes problem: A unified approach
    • Stenberg R. Analysis of mixed finite element methods for the Stokes problem: a unified approach. Mathematics of Computation 1984; 42:9-23.
    • (1984) Mathematics of Computation , vol.42 , pp. 9-23
    • Stenberg, R.1
  • 23
    • 0025507123 scopus 로고
    • A technique for analysing finite element methods for viscous incompressible flow
    • Stenberg R. A technique for analysing finite element methods for viscous incompressible flow. International Journal for Numerical Methods in Fluids 1990; 11:935-948.
    • (1990) International Journal for Numerical Methods in Fluids , vol.11 , pp. 935-948
    • Stenberg, R.1
  • 24
    • 34250962104 scopus 로고
    • Allgemeine kontinuumstheorie der versetzungen und eigenspannungen
    • Kröner E. Allgemeine kontinuumstheorie der versetzungen und eigenspannungen. Archive for Rational Mechanics and Analysis 1959; 4:273-334.
    • (1959) Archive for Rational Mechanics and Analysis , vol.4 , pp. 273-334
    • Kröner, E.1
  • 27
    • 85095827382 scopus 로고    scopus 로고
    • Finite elements in computational electromagnetism
    • Cambridge University Press: Cambridge
    • Hiptmair R. Finite elements in computational electromagnetism. Acta Numerica, vol. 11. Cambridge University Press: Cambridge, 2002; 237-339.
    • (2002) Acta Numerica , vol.11 , pp. 237-339
    • Hiptmair, R.1
  • 28
    • 1542355827 scopus 로고    scopus 로고
    • Ph.D. Thesis, California Institute of Technology
    • Hirani A. Discrete exterior calculus. Ph.D. Thesis, California Institute of Technology, 2003.
    • (2003) Discrete exterior calculus
    • Hirani, A.1
  • 34
    • 35248884115 scopus 로고    scopus 로고
    • Discrete differential operators and analysis in incompressible elasticity
    • in press
    • Hauret P, Kuhl E, Ortiz M. Discrete differential operators and analysis in incompressible elasticity, in press.
    • Hauret, P.1    Kuhl, E.2    Ortiz, M.3
  • 36
    • 35248850892 scopus 로고    scopus 로고
    • Bernardi C, Maday Y, Patera AT: Domain decomposition by the mortar element method. In Asymptotic and Numerical Methods for Partial Differential Equations with Critical Parameters, Kaper HG, Garbey M (eds). Kluwer Academic Publishers: N.A.T.O. ASI, 1993; 269-286.
    • Bernardi C, Maday Y, Patera AT: Domain decomposition by the mortar element method. In Asymptotic and Numerical Methods for Partial Differential Equations with Critical Parameters, Kaper HG, Garbey M (eds). Kluwer Academic Publishers: N.A.T.O. ASI, 1993; 269-286.
  • 37
    • 0041800397 scopus 로고    scopus 로고
    • The mortar finite element method with Lagrange multipliers
    • Ben Belgacem F. The mortar finite element method with Lagrange multipliers. Numerische Mathematik 1999; 84:173-197.
    • (1999) Numerische Mathematik , vol.84 , pp. 173-197
    • Ben Belgacem, F.1
  • 40
    • 0040823837 scopus 로고
    • A mixed method of the stress-displacement pressure type for solving incompressible plane-strain viscoelasticity problems
    • Ruas V. A mixed method of the stress-displacement pressure type for solving incompressible plane-strain viscoelasticity problems. Comptes Rendus à l'Académie des Sciences Paris 1985; II(301):1171-1174.
    • (1985) Comptes Rendus à l'Académie des Sciences Paris , vol.2 , Issue.301 , pp. 1171-1174
    • Ruas, V.1
  • 45
    • 11944251074 scopus 로고    scopus 로고
    • F-bar-based linear triangles and tetrahedra for finite strain analysis of nearly incompressible solides. Part i: Formulation and benchmarking
    • De Souza Neto EA, Pires FM, Owen DRJ. F-bar-based linear triangles and tetrahedra for finite strain analysis of nearly incompressible solides. Part i: formulation and benchmarking. International Journal for Numerical Methods in Engineering 2005; 62:353-383.
    • (2005) International Journal for Numerical Methods in Engineering , vol.62 , pp. 353-383
    • De Souza Neto, E.A.1    Pires, F.M.2    Owen, D.R.J.3
  • 46
    • 0025399187 scopus 로고
    • Formulation of implicit finite-element methods for multiplicative finite deformation plasticity
    • Moran B, Ortiz M, Shih CF. Formulation of implicit finite-element methods for multiplicative finite deformation plasticity. International Journal for Numerical Methods in Engineering 1990; 29(3):483-514.
    • (1990) International Journal for Numerical Methods in Engineering , vol.29 , Issue.3 , pp. 483-514
    • Moran, B.1    Ortiz, M.2    Shih, C.F.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.