Veronica Anaya, Zoa De Wijn, David Mora, Ricardo Ruiz-Baier:
Mixed displacement-rotation-pressure formulations for elasticity
We propose a family of mixed finite element and finite volume element methods for the approximation of linear elastostatics, formulated in terms of displacement, rotation vector, and pressure. The unique solvability of the three-field continuous formulation, as well as the invertibility and stability of the proposed Galerkin and Petrov-Galerkin methods, is established thanks to the Babuska-Brezzi theory. Optimal a priori error estimates are derived using norms robust with respect to the Lamé constants, turning these numerical methods particularly appealing for nearly incompressible materials. We exemplify the accuracy and applicability of the new formulation and the mixed schemes by conducting a number of computational tests in 2D and 3D.