## Dual-mixed $$hp$$ finite element methods using first-order stress functions and rotations.(English)Zbl 0980.74057

From the summary: We consider a two-field dual-mixed variational formulation of three-dimensional elasticity in terms of non-symmetric stress tensor and skew-symmetric rotation tensor. The translational equilibrium equations are satisfied a priori by introducing the tensor of first-order stress functions. It is pointed out that the use of six properly chosen first-order stress function components leads to a (three-dimensional) weak formulation, which is analogous to displacement-pressure formulation of elasticity and velocity-pressure formulation of Stokes flow. The subsequent selection of stable mixed $$hp$$ finite element spaces is based on this analogy.

### MSC:

 74S05 Finite element methods applied to problems in solid mechanics 74B10 Linear elasticity with initial stresses
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