Residual estimates for post-processors in elliptic problems

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Dedner, Andreas, Giesselmann, Jan, Pryer, Tristan and Ryan, Jennifer K. (2021) Residual estimates for post-processors in elliptic problems. Journal of Scientific Computing, 88 (2). ISSN 0885-7474

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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 post-processing techniques to enable efficient 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-Conserving filter and superconvergent patch recovery. Extensive numerical tests are conducted that confirm our analytic findings.

Item Type:	Article
Uncontrolled Keywords:	a posteriori error bound,adaptivity,discontinuous galerkin,finite element method,post-processing,siac filter,superconvergent patch recovery,software,theoretical computer science,numerical analysis,engineering(all),computational theory and mathematics,computational mathematics,applied mathematics ,/dk/atira/pure/subjectarea/asjc/1700/1712
Faculty \ School:	Faculty of Science > School of Mathematics
UEA Research Groups:	Faculty of Science > Research Groups > Fluid and Solid Mechanics
Related URLs:	http://www.scopus.com/inward/record.url?... https://arxiv.org/abs/1906.04658
Depositing User:	LivePure Connector
Date Deposited:	14 Oct 2022 10:33
Last Modified:	22 Oct 2022 04:50
URI:	https://ueaeprints.uea.ac.uk/id/eprint/89072
DOI:	10.1007/s10915-021-01502-2

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