  For the planar Navier--Lam\'e equation in mixed form with symmetric stress
tensors, we prove the uniform quasi-optimal convergence of an adaptive method
based on the hybridized mixed finite element proposed in [Gong, Wu, and Xu:
Numer.~Math., 141 (2019), pp.~569--604]. The main ingredients in the analysis
consist of a discrete a posteriori upper bound and a quasi-orthogonality result
for the stress field under the mixed boundary condition. Compared with existing
adaptive methods, the proposed adaptive algorithm could be directly applied to
the traction boundary condition and be easily implemented.
