Recovery procedures in error estimation and adaptivity Part I: Adaptivity in linear problems Original Research Article

The procedures of error estimation using stress or gradient recovery were introduced by Zienkiewicz and Zhu in 1987 [3]and with the improvement of recovery procedures (introduction of Superconvergent Patch Recovery (SPR)) since that date the authors have succeeded in making these error estimators the most robust of those currently available. Very recently introduced methods of recovery such as REP (Recovery by Equilibrium in Patches) allow general application. In this paper the general idea of using recovery based error estimation in adaptive procedure of linear problems is explained through which the latest developments in recovery techniques is described. The fundamental basis of a ‘patch test’ introduced by Babuška et al. [11–14]is explained and applied to the recovery based error estimators using both SPR and REP.