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Analysis and finite element approximation of compressible and incompressible linear isotropic elasticity based upon a variational principle. (English) Zbl 0688.73044
Summary: We propose a variational principle for compressible and incompressible linear isotropic elasticity involving four dependent variables: the strain tensor, the augmented stress tensor, pressure and displacement. The variational formulation derived from the principle is analyzed employing a general result due to F. Brezzi [Revue Franç. Automat. Inform. Rech. Opérat. 8, R-2, 129-151 (1974; Zbl 0338.90047)]. Finite element methods using the Galerkin and SBB methods are shown to converge for a wide family of finite element interpolations.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
65K10 Numerical optimization and variational techniques
49M15 Newton-type methods
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