  In this paper, a reliable a posteriori error estimator for a model problem of
elastoplasticity with linear kinematic hardening is derived, which satisfies
some (local) efficiency estimates. It is applicable to any discretization that
is conforming with respect to the displacement field and the plastic strain.
Furthermore, the paper presents $hp$-finite element discretizations relying on
a variational inequality as well as on a mixed variational formulation and
discusses their equivalence by using biorthogonal basis functions. Numerical
experiments demonstrate the applicability of the theoretical findings and
underline the potential of $h$- and $hp$-adaptive finite element
discretizations for problems of elastoplasticity.
