Residual Estimates for Post-processors in Elliptic Problems

Abstract In this work we examine a posteriori error control for post-processed approximations to elliptic boundary value problems. We introduce class of post-processing operator that “tweaks” wide variety existing techniques enable efficient and reliable bounds be proven. This ultimately results in optimal all manner reconstruction operators, including those superconverge. showcase our by applying them two classes very popular the Smoothness-Increasing Accuracy-Conserving filter superconvergent patch recovery. Extensive numerical tests are conducted confirm analytic findings.