On an unconventional variational method for solving the problem of linear elasticity with Neumann or periodic boundary conditions

Michal Křížek; Zdeněk Milka

Banach Center Publications (1994)

  • Volume: 29, Issue: 1, page 65-77
  • ISSN: 0137-6934

Abstract

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A new variational formulation of the linear elasticity problem with Neumann or periodic boundary conditions is presented. This formulation does not require any quotient spaces and is advisable for finite element approximations.

How to cite

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Křížek, Michal, and Milka, Zdeněk. "On an unconventional variational method for solving the problem of linear elasticity with Neumann or periodic boundary conditions." Banach Center Publications 29.1 (1994): 65-77. <http://eudml.org/doc/262855>.

@article{Křížek1994,
abstract = {A new variational formulation of the linear elasticity problem with Neumann or periodic boundary conditions is presented. This formulation does not require any quotient spaces and is advisable for finite element approximations.},
author = {Křížek, Michal, Milka, Zdeněk},
journal = {Banach Center Publications},
keywords = {finite element approximations; Lipschitz boundary; Sobolev space},
language = {eng},
number = {1},
pages = {65-77},
title = {On an unconventional variational method for solving the problem of linear elasticity with Neumann or periodic boundary conditions},
url = {http://eudml.org/doc/262855},
volume = {29},
year = {1994},
}

TY - JOUR
AU - Křížek, Michal
AU - Milka, Zdeněk
TI - On an unconventional variational method for solving the problem of linear elasticity with Neumann or periodic boundary conditions
JO - Banach Center Publications
PY - 1994
VL - 29
IS - 1
SP - 65
EP - 77
AB - A new variational formulation of the linear elasticity problem with Neumann or periodic boundary conditions is presented. This formulation does not require any quotient spaces and is advisable for finite element approximations.
LA - eng
KW - finite element approximations; Lipschitz boundary; Sobolev space
UR - http://eudml.org/doc/262855
ER -

References

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  1. [1] I. Babuška Uncertainties in engineering design: mathematical theory and numerical experience, in: The Optimal Shape, J. Bennett and M. M. Botkin (eds.), Plenum Press, 1986; also in: Technical Note BN-1044, Univ. of Maryland, 1985, 1-35. 
  2. [2] I. Hlaváček and J. Nečas, On inequalities of Korn's type, I, Boundary-value problems for elliptic systems of partial differential equations, II, Applications to linear elasticity, Arch. Rational Mech. Anal. 36 (1970), 305-311, 312-334. Zbl0193.39001
  3. [3] M. Křížek, Conforming equilibrium finite element methods for some elliptic plane problems, RAIRO Numer. Anal. 17 (1983), 35-65. Zbl0541.76003
  4. [4] M. Křížek and P. Neittaanmäki, Finite Element Approximation of Variational Problems and Applications, Longman, Harlow 1990. 
  5. [5] M. Křížek, P. Neittaanmäki and M. Vondrák, A nontraditional approach for solving the Neumann problem by the finite element method, Mat. Apl. Comput. 11 (1992), 31-40. Zbl0771.65070
  6. [6] D. F. Luenberger, Hyperbolic pairs in the method of conjugate gradients, SIAM J. Appl. Math. 17 (1969), 1263-1267. Zbl0187.09704
  7. [7] J. Nečas, Les méthodes directes en théorie des équations elliptiques, Academia, Prague 1967. 
  8. [8] J. Nečas and I. Hlaváček, Mathematical Theory of Elastic and Elasto-plastic Bodies: An Introduction, Elsevier, Amsterdam 1981. 
  9. [9] J. Taufer, Lösung der Randwertprobleme für Systeme von linearen Differentialgleichungen, Academia, Prague 1973. Zbl0276.34009
  10. [10] R. Temam, Infinite-dimensional Dynamical Systems in Mechanics and Physics, Springer, Berlin 1988. Zbl0662.35001
  11. [11] D. E. Ward, Exact penalties and sufficient conditions for optimality in nonsmooth optimization, J. Optim. Theory Appl. 57 (1988), 485-499. Zbl0621.90081

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