Abstract
This chapter addresses the numerical approximation of the mathematical model for a linear elastic material. The model is able to treat both compressible and incompressible regimes under a unified framework known as Herrmann formulation of linear elasticity, based on the introduction of a further dependent variable, called pressure parameter, in addition to the solid displacement. The pressure parameter coincides with the hydrostatic pressure in the incompressible limit, where the Herrmann model formally coincides with the Stokes equations for a viscous incompressible fluid in stationary conditions. Weak formulation and finite element approximation of the Herrmann model are illustrated and the compatibility between the approximation spaces for displacement and pressure is analyzed in order to provide sufficient conditions for the numerical method to be stable and convergent. Examples of stable and unstable finite element spaces for displacement and pressure are discussed and computationally investigated in the solution of two-dimensional test cases.
Published Version
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