A posteriori error estimation has become essential to assess the accuracy and robustness of Finite Element simulations. Furthermore, it is a key feature for any adaptivity procedure.

The present work aims for an unified framework for different Reduction of the Residual to Local Patch approaches with Dirichlet boundary conditions, allowing its comparison and improvement through hybridization. The paper introduces the ideas of treating the residual as an element-wise pre-stress for the error problem rather than averaging patch contributions and decoupling the error fluctuation inside an element from the error fluctuation over its edges.

Computational results in terms of accuracy, computational time and cost-efficiency for the different approaches and some new estimates based on the combination of the known and new concepts are included. Poisson and linear elasticity problems are used to compare the methods.