RESIDUAL ESTIMATES FOR POST-PROCESSORS IN ELLIPTIC PROBLEMS

Andreas Dedner, Jan Giesselmann, Tristan Pryer, Jennifer Ryan

Research output: Contribution to journalArticle

Abstract

In this work we examine a posteriori error control for post-processed approximations
to elliptic boundary value problems. We introduce a class of post-processing operator that "tweaks" a wide variety of existing postprocessing techniques to enable ecient and reliable a posteriori bounds to be proven. This ultimately results in optimal error control for all manner of reconstruction operators, including those that superconverge.
We showcase our results by applying them to two classes of very popular reconstruction operators, the Smoothness-Increasing Accuracy-Enhancing lter and Superconvergent Patch Recovery. Extensive numerical tests are conducted that conrm our analytic ndings.
Original languageEnglish
JournalSIAM Journal on Scientific Computing
Publication statusSubmitted - 11 Jun 2019

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