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Finite element approximation of a new variational principle for compressible and incompressible linear isotropic elasticity. (English) Zbl 0749.73076
Summary: Stability conditions are described to analyze a variational formulation emanating from a variational principle for linear isotropic elasticity. The variational principle is based on four dependent variables (namely, the strain tensor, augmented stress, pressure, and displacement) and is shown to be valid for any compressibility including the incompressible limit. An improved convergence error analysis is established for a Galerkin-least-squares method based upon these four variables. The analysis presented establishes convergence for a wide choice of combinations of finite element interpolations.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
74P10 Optimization of other properties in solid mechanics
74B05 Classical linear elasticity
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