  It is well known that via the augmented Lagrangian method, one can solve
Stokes' system by solving the nearly incompressible linear elasticity equation.
In this paper, we show that the converse holds, and approximate the inverse of
the linear elasticity operator with a convex linear combination of
parameter-free operators. In such a way, we construct a uniform preconditioner
for linear elasticity for all values of the Lam\'{e} parameter $\lambda\in
[0,\infty)$. Numerical results confirm that by using inf-sup stable
finite-element spaces for the solution of Stokes' equations, the proposed
preconditioner is robust in $\lambda$.
