  Elliptic reconstruction property, originally introduced by Makridakis and
Nochetto for linear parabolic problems, is a well-known tool to derive optimal
a posteriori error estimates. No such results are known for nonlinear and
nonsmooth problems such as parabolic variational inequalities (VIs). This
article establishes the elliptic reconstruction property for parabolic VIs and
derives a posteriori error estimates in $L^{\infty}(0,T;L^{2}(\Omega))$. The
estimator consists of discrete complementarity terms and standard residual. As
an application, the residual-type error estimates are presented.
