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CSFEM for Large Deformation of Solids: From Hilbert Complexes to Numerical Stability Open Access

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We study the stability of a class of three-field mixed finite element methods for nonlinear elasticity called CSFEMs near regular solutions. To this end, we write suitable material-independent and material-dependent inf-sup conditions. The material-independent condition is only a necessary condition for the stability while the material-depend one is sufficient as well. By considering several combinations of first-order and second-order elements, we study the validity of these inf-sup conditions by using singular values associated to the matrix form of the inf-sup conditions.

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