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We are concerned with an Interior Penalty Discontinuous Galerkin (IPDG) approximation of the  p -Laplace equation and an equilibrated a posteriori error estimator. The IPDG method can be derived from a discretization of the associated minimization problem involving appropriately defined reconstruction operators. The equilibrated a posteriori error estimator provides an upper bound for the discretization error in the broken  W  1, p   norm and relies on the construction of an equilibrated flux in terms of a numerical flux function associated with the mixed formulation of the IPDG approximation. The relationship with a residual-type a posteriori error estimator is established as well. Numerical results illustrate the performance of both estimators.

An equilibrated a posteriori error estimator for an Interior Penalty Discontinuous Galerkin approximation of the p -Laplace problem