Averaging technique for FE – a posteriori error control in elasticity. Part I: Conforming FEM Original Research Article

Averaging techniques are popular tools in adaptive finite element methods for the numerical treatment of second-order partial differential equations since they provide efficient a posteriori error estimates by a simple postprocessing. In this paper, the reliability of any averaging estimator is shown for low order finite element methods in elasticity. Theoretical and numerical evidence supports that the reliability is up to the smoothness of given right-hand sides and independent of the structure of a shape-regular mesh.