  The Gradient Scheme framework provides a unified analysis setting for many
different families of numerical methods for diffusion equations. We show in
this paper that the Gradient Scheme framework can be adapted to elasticity
equations, and provides error estimates for linear elasticity and convergence
results for non-linear elasticity. We also establish that several classical and
modern numerical methods for elasticity are embedded in the Gradient Scheme
framework, which allows us to obtain convergence results for these methods in
cases where the solution does not satisfy the full $H^2$-regularity or for
non-linear models.
