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Inf-sup stable finite element pairs based on dual meshes and bases for nearly incompressible elasticity. (English) Zbl 1160.74046
Summary: We consider finite element methods based on simplices to solve the problem of nearly incompressible elasticity. Two different approaches based, respectively, on dual meshes and dual bases are presented, where in both approaches pressure is discontinuous and can be statically condensed out from the system. These novel approaches lead to displacement-based low-order finite element methods for nearly incompressible elasticity based on rigorous mathematical framework. Numerical results demonstrate the efficiency of the approach.

74S05 Finite element methods applied to problems in solid mechanics
74B05 Classical linear elasticity
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