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Refined mixed finite element method for the elasticity problem in a polygonal domain
Author(s) -
Farhloul M.,
Paquet L.
Publication year - 2002
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.10009
Subject(s) - mathematics , sobolev space , lagrange multiplier , elasticity (physics) , finite element method , mathematical analysis , displacement field , geometry , mathematical optimization , materials science , physics , composite material , thermodynamics
Abstract The purpose of this article is to study a mixed formulation of the elasticity problem in plane polygonal domains and its numerical approximation. In this mixed formulation the strain tensor is introduced as a new unknown and its symmetry is relaxed by a Lagrange multiplier, which is nothing else than the rotation. Because of the corner points, the displacement field is not regular in general in the vicinity of the vertices but belongs to some weighted Sobolev space. Using this information, appropriate refinement rules are imposed on the family of triangulations in order to recapture optimal error estimates. Moreover, uniform error estimates in the Lamé coefficient λ are obtained for λ large. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 323–339, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/num.10009