Mixed formulation for elastic problems - existence, approximation, and applications to Poisson structures

Julian Ławrynowicz; Alain Mignot; Loucas Papaloucas; Claude Surry

Banach Center Publications (1996)

  • Volume: 37, Issue: 1, page 343-349
  • ISSN: 0137-6934

Abstract

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A mixed formulation is given for elastic problems. Existence and uniqueness of the discretized problem are given for conformal continuous interpolations for the stress tensor components and for the components of the displacement vector. A counterpart of the problem is discussed in the case of an even-dimensional Euclidean space with an associated Hamiltonian vector field and the Poisson structure. For conformal interpolations of the same order the question remains open.

How to cite

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Ławrynowicz, Julian, et al. "Mixed formulation for elastic problems - existence, approximation, and applications to Poisson structures." Banach Center Publications 37.1 (1996): 343-349. <http://eudml.org/doc/208612>.

@article{Ławrynowicz1996,
abstract = {A mixed formulation is given for elastic problems. Existence and uniqueness of the discretized problem are given for conformal continuous interpolations for the stress tensor components and for the components of the displacement vector. A counterpart of the problem is discussed in the case of an even-dimensional Euclidean space with an associated Hamiltonian vector field and the Poisson structure. For conformal interpolations of the same order the question remains open.},
author = {Ławrynowicz, Julian, Mignot, Alain, Papaloucas, Loucas, Surry, Claude},
journal = {Banach Center Publications},
keywords = {discretized problem; conformal continuous interpolation; stress tensor; displacement vector; even-dimensional Euclidean space; Hamiltonian vector field},
language = {eng},
number = {1},
pages = {343-349},
title = {Mixed formulation for elastic problems - existence, approximation, and applications to Poisson structures},
url = {http://eudml.org/doc/208612},
volume = {37},
year = {1996},
}

TY - JOUR
AU - Ławrynowicz, Julian
AU - Mignot, Alain
AU - Papaloucas, Loucas
AU - Surry, Claude
TI - Mixed formulation for elastic problems - existence, approximation, and applications to Poisson structures
JO - Banach Center Publications
PY - 1996
VL - 37
IS - 1
SP - 343
EP - 349
AB - A mixed formulation is given for elastic problems. Existence and uniqueness of the discretized problem are given for conformal continuous interpolations for the stress tensor components and for the components of the displacement vector. A counterpart of the problem is discussed in the case of an even-dimensional Euclidean space with an associated Hamiltonian vector field and the Poisson structure. For conformal interpolations of the same order the question remains open.
LA - eng
KW - discretized problem; conformal continuous interpolation; stress tensor; displacement vector; even-dimensional Euclidean space; Hamiltonian vector field
UR - http://eudml.org/doc/208612
ER -

References

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  5. [5] V. Girault and P.-A. Raviart, Finite Element Methods for Navier-Stokes Equations, Theory and Algorithms, Springer Series in Computational Matematics, Springer, Berlin 1986. Zbl0585.65077
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  11. [11] J. Ławrynowicz and L. Wojtczak in cooperation with S. Koshi and O. Suzuki, Stochastical mechanics of particle systems in Clifford-analytical formulation related to Hurwitz pairs of dimension (8,5), in: Deformations of Mathematical Structures II. Hurwitz-Type Structures and Applications to Surface Physics, J. Ławrynowicz (ed.), Kluwer Academic Publishers, Dordrecht-Boston-London 1994, pp. 213-262. Zbl0828.60081
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  14. [14] G. Lube, Stabilized Galerkin finite element methods for convection dominated and incompressible flow problems, in: Numerical Analysis and Mathematical Modelling, J.K. Kowalski and A. Wakulicz (eds.), Banach Center Publications, 29 Pol. Acad. Sci. - Inst. of Math., Warszawa 1994, pp. 85-104. Zbl0801.76046
  15. [15] A.-L. Mignot and C. Surry, A mixed finite element family in plane elasticity, Appl. Math. Mod. 5 (1981), 259-262. 
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  18. [18] L. C. Papaloucas, Polynomial Poisson subalgebras, Bull. Soc. Sci. Lettres Łódź 45, Sér. Rech. Déform. 19 (1995), 57-64. 

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