This study considers local post-processing strategies on contiguous patches of cells (or elements) and the properties and applications of the resulting approximations. For instance, one is interested in accuracy of recovered gradients and in their use in constructing error estimators or error indicators for adaptivity. Hence, there are two distinct concepts: (1) The improved quality of recovered gradients on a local patch; and/or (2) the use of local recovered quantities to construct error indicators to guide adaptive refinement schemes. We present a framework generalizing existing strategies for averaging operators and discuss the advantages of this framework in a parallel computing environment. Copyright © 2011 John Wiley & Sons, Ltd.