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Residual estimates for post-processors in elliptic problems
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Dedner, Andreas, Giesselmann, Jan, Pryer, Tristan and Ryan, Jennifer K. (2020) Residual estimates for post-processors in elliptic problems. Journal of Scientific Computing, 88 . 34. doi:10.1007/s10915-021-01502-2 ISSN 0885-7474.
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Official URL: https://doi.org/10.1007/s10915-021-01502-2
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-Enhancing filter and Superconvergent Patch Recovery. Extensive numerical tests are conducted that confirm our analytic findings.
| Item Type: | Journal Article | |||||||||
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| Subjects: | Q Science > QA Mathematics | |||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||
| Library of Congress Subject Headings (LCSH): | Elliptic functions, Finite element method , Differential equations, Partial | |||||||||
| Journal or Publication Title: | Journal of Scientific Computing | |||||||||
| Publisher: | Springer New York LLC | |||||||||
| ISSN: | 0885-7474 | |||||||||
| Official Date: | 21 June 2020 | |||||||||
| Dates: |
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| Volume: | 88 | |||||||||
| Article Number: | 34 | |||||||||
| DOI: | 10.1007/s10915-021-01502-2 | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | Published | |||||||||
| Access rights to Published version: | Open Access (Creative Commons) | |||||||||
| Date of first compliant deposit: | 6 January 2021 | |||||||||
| Date of first compliant Open Access: | 7 July 2021 | |||||||||
| RIOXX Funder/Project Grant: |
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