In a posteriori error estimation, one tries to quantify the error of an approximate solution of a partial differential equation in terms of quantities that are `computable'. Typically, so-called oscillation terms spoil the equivalence between error and estimator in that they may be larger than the error. As a consequence, they also spoil subsequent results on adaptive finite elements.

This talks considers linear finite element solutions to the Poisson problem and presents an a posteriori error analysis, where the oscillation terms are dominated by the error, irrespective of mesh fineness and extra regularity of the given data.