PEERS: A new mixed finite element for plane elasticity
Purchase on Springer.com
$39.95 / €34.95 / £29.95*
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.
A mixed finite element procedure for plane elasticity is introduced and analyzed. The symmetry of the stress tensor is enforced through the introduction of a Lagrange multiplier. An additional Lagrange multiplier is introduced to simplify the linear algebraic system. Applications are made to incompressible elastic problems and to plasticity problems.
Supplementary Material (0)
- M. Amara and J. M. Thomas, Equilibrium finite elements for the linear elastic problem. Numer. Math.,33 (1979), 367–383. CrossRef
- D. N. Arnold and F. Brezzi, Mixed and nonconforming finite element methods: implementation, postprocessing, and error estimates. RAIRO Anal. Numér.,19 (1985).
- D. N. Arnold, J. Douglas, Jr., and C. P. Gupta, A family of higher order finite element methods for plane elasticity. Numer. Math.,45 (1984), 1–22. CrossRef
- D. N. Arnold, L. R. Scott, and M. Vogelius, Regular solutions of divu=f with Dirichlet boundary conditions on a polygon. Tech. Note, Univ. Maryland, to appear.
- F. Brezzi, On the existence, uniqueness, and approximation of saddle point problems arising from Lagrangian multipliers. RAIRO Anal. Numér.,2 (1974), 129–151.
- P. Clément, Approximation by finite element functions using local regularization. RAIRO Anal. Numér.,9 (1975), 33–76.
- J. Douglas, Jr., and F. A. Milner, Interior and superconvergence estimates for mixed methods for second order elliptic problems, to appear in RAIRO Anal. Numér.
- J. Douglas, Jr., and J. E. Roberts, Mixed finite element methods for second order elliptic problems, Mat. Aplic. Comp.,1 (1982), 91–103.
- J. Douglas, Jr., and J. E. Roberts, Global estimates for mixed methods for second order elliptic equations, to appear in Math. Comput.
- I. Ekeland and R. Temam,Analyse Convexe et Problèmes Variationnels. Dunod-Gauthier-Villars, Paris, 1974.
- R. S. Falk and J. E. Osborn, Error estimates for mixed methods. RAIRO Anal. Numér.,14 (1980), 309–324.
- M. Fortin, An analysis of the convergence of mixed finite element methods. RAIRO Anal. Numér.,11 (1977), 341–354.
- B. X. Fraeijs de Veubeke, Stress function approach. World Congress on the Finite Element Method in Structural Mechanics, Bornemouth, 1975.
- C. Johnson, On finite element methods for plasticity problems. Numer. Math.,26 (1976), 79–84. CrossRef
- C. Johnson, A mixed finite element method for plasticity with hardening. SIAM J. Numer. Anal.,14 (1977), 575–583. CrossRef
- C. Johnson, Existence theorems for plasticity problems. J. Math. Pure Appl.,55 (1976), 431–444.
- C. Johnson and B. Mercier, Some equilibrium finite element methods for two-dimensional elasticity problems. Numer. Math.,30 (1978), 103–116. CrossRef
- P. A. Raviart and J. M. Thomas, A mixed finite element method for second order elliptic problems.Mathematical Aspects of the Finite Element Method (eds., I. Galligani and E. Magenes), Lecture Notes in Math. 606, Springer-Verlag, 1977.
- M. Vogelius, An analysis of thep-version of the finite element method for nearly incompressible materials. Uniformly valid, optimal order estimates. Numer. Math.,41 (1983), 39–53. CrossRef
About this Article
- PEERS: A new mixed finite element for plane elasticity
Japan Journal of Applied Mathematics
Volume 1, Issue 2 , pp 347-367
- Cover Date
- Print ISSN
- Additional Links
- finite element methods
- plane elasticity
- Author Affiliations
- 1. Department of Mathematics, University of Maryland, 20742, College Park, MD, USA
- 2. Istituto di Analisi Numerica, Palazzo dell’Università, 27100, Pavia, Italy
- 3. Department of Mathematics, University of Chicago, 60637, Chicago, IL, USA