A Hu–Washizu stabilization-free Virtual Element Method for 3D linear elasticity with star-convex polyhedrons
Résumé
We present a Hu-Washizu stabilization-free Virtual Element Method for three-dimensional linear elasticity. To that end, the discrete formulation of the problem is obtained using the three-fields Hu-Washizu variational approach. The discrete displacement space is given as an enhanced virtual element space which introduces a new projector that only requires integration over the edges of the element. The well-posedness of the proposed formulation is studied using an eigenvalue analysis and its performances are assessed on various 3D linear elasticity problems. The numerical examples use star-convex elements and, for the first time in the literature, include concave cases.