Dedner, Andreas ; Giesselmann, Jan ; Pryer, Tristan ; Ryan, Jennifer K. (2019)
Residual estimates for post-processors in elliptic problems.
doi: 10.48550/arXiv.1906.04658
Report, Bibliographie
Kurzbeschreibung (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.
| Typ des Eintrags: | Report |
|---|---|
| Erschienen: | 2019 |
| Autor(en): | Dedner, Andreas ; Giesselmann, Jan ; Pryer, Tristan ; Ryan, Jennifer K. |
| Art des Eintrags: | Bibliographie |
| Titel: | Residual estimates for post-processors in elliptic problems |
| Sprache: | Englisch |
| Publikationsjahr: | 11 Juni 2019 |
| Verlag: | arXiV |
| Reihe: | Numerical Analysis |
| Auflage: | 1. Version |
| DOI: | 10.48550/arXiv.1906.04658 |
| URL / URN: | https://arxiv.org/abs/1906.04658 |
| Kurzbeschreibung (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. |
| Zusätzliche Informationen: | Preprint |
| Fachbereich(e)/-gebiet(e): | 04 Fachbereich Mathematik 04 Fachbereich Mathematik > Numerik und wissenschaftliches Rechnen |
| Hinterlegungsdatum: | 21 Okt 2019 09:39 |
| Letzte Änderung: | 29 Mai 2024 10:18 |
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