  This paper presents a family of mixed finite elements on triangular grids for
solving the classical Hellinger-Reissner mixed problem of the elasticity
equations. In these elements, the matrix-valued stress field is approximated by
the full $C^0$-$P_k$ space enriched by $(k-1)$ $H(\d)$ edge bubble functions on
each internal edge, while the displacement field by the full discontinuous
$P_{k-1}$ vector-valued space, for the polynomial degree $k\ge 3$. The main
challenge is to find the correct stress finite element space matching the full
$C^{-1}$-$P_{k-1}$ displacement space. The discrete stability analysis for the
inf-sup condition does not rely on the usual Fortin operator, which is
difficult to construct. It is done by characterizing the divergence of local
stress space which covers the $P_{k-1}$ space of displacement orthogonal to the
local rigid-motion. The well-posedness condition and the optimal a priori error
estimate are proved for this family of finite elements. Numerical tests are
presented to confirm the theoretical results.
