Before revision:  We derive an a posteriori estimator of the energy error between the solutions of the exact and the defeatured geometries in R^n,  that is simple, efficient and reliable up to oscillations.
After revision:  We derive an a posteriori estimator of the energy error between the solutions of the exact and the defeatured geometries in R^n, n\in\{2,3\ that is simple, efficient and reliable up to oscillations.