  A face-centred finite volume (FCFV) method is proposed for the linear
elasticity equation. The FCFV is a mixed hybrid formulation, featuring a system
of first-order equations, that defines the unknowns on the faces (edges in two
dimensions) of the mesh elements. The symmetry of the stress tensor is strongly
enforced using the well-known Voigt notation and the displacement and stress
fields inside each cell are obtained element-wise by means of explicit
formulas. The resulting FCFV method is robust and locking-free in the nearly
incompressible limit. Numerical experiments in two and three dimensions show
optimal convergence of the displacement and the stress fields without any
reconstruction. Moreover, the accuracy of the FCFV method is not sensitive to
mesh distortion and stretching. Classical benchmark tests including Kirch's
plate and Cook's membrane problems in two dimensions as well as three
dimensional problems involving shear phenomenons, pressurised thin shells and
complex geometries are presented to show the capability and potential of the
proposed methodology.

Numerical Analysis;Computational Engineering, Finance, and Science;Numerical Analysis