We revisit the a posteriori error analysis of discontinuous
Galerkin methods for the obstacle problem derived in
[Math. Comput. (2013), DOI 10.1090/S0025-5718-2013-02728-7].
Under a mild assumption on the trace of obstacle, we
derive a reliable a posteriori error estimator which does
not involve min/max functions. A key in this approach is an
auxiliary problem with discrete obstacle. Applications to various
discontinuous Galerkin finite element methods are presented.
Numerical experiments show that the new estimator obtained in this
article performs better.