An improved REP recovery and the effectivity robustness test

We present in this paper a modi ed form of the REP gradient recovery process recently published.1 This new form is not only cheaper but has a much improved performance|which equals and occasionally exceeds the performance of the SPR (Superconvergent Patch Recovery) method.2{4 The comparisons are based on the robustness test originally proposed by Babu ska et al.5{8 This test is described brie y in a manner suitable for those who nd some aspects of modern mathematics di cult to follow. The result and comparison of the tests for various repeatable patches with regular and irregular element distribution are made with SPR and the `oldʹ form of REP and are based on the general error estimator introduced by Zienkiewicz and Zhu in 1987.9