Some p-robust a posteriori error estimates based on auxiliary spaces
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909900289867776 |
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| author | Li, Yuwen |
| author_facet | Li, Yuwen |
| contents | This work develops polynomial-degree-robust (p-robust) equilibrated a posteriori error estimates for $H(\rm curl)$, $H(\rm div)$ and $H(\rm divdiv)$ problems, based on $H^1$ auxiliary space decomposition. The proposed framework employs auxiliary space preconditioning and regular decompositions to decompose the finite element residual into $H^{-1}$ residuals that are further controlled by classical p-robust equilibrated a posteriori error analysis. As a result, we obtain novel and simple p-robust a posteriori error estimates of $H(\rm curl)$/$H(\rm div)$ conforming methods and mixed methods for the biharmonic equation. In addition, we prove guaranteed a posteriori upper error bounds under convex domains or certain boundary conditions. Numerical experiments demonstrate the effectiveness and p-robustness of the proposed error estimators for the Nédélec edge element methods and the Hellan--Herrmann--Johnson methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_06603 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some p-robust a posteriori error estimates based on auxiliary spaces Li, Yuwen Numerical Analysis This work develops polynomial-degree-robust (p-robust) equilibrated a posteriori error estimates for $H(\rm curl)$, $H(\rm div)$ and $H(\rm divdiv)$ problems, based on $H^1$ auxiliary space decomposition. The proposed framework employs auxiliary space preconditioning and regular decompositions to decompose the finite element residual into $H^{-1}$ residuals that are further controlled by classical p-robust equilibrated a posteriori error analysis. As a result, we obtain novel and simple p-robust a posteriori error estimates of $H(\rm curl)$/$H(\rm div)$ conforming methods and mixed methods for the biharmonic equation. In addition, we prove guaranteed a posteriori upper error bounds under convex domains or certain boundary conditions. Numerical experiments demonstrate the effectiveness and p-robustness of the proposed error estimators for the Nédélec edge element methods and the Hellan--Herrmann--Johnson methods. |
| title | Some p-robust a posteriori error estimates based on auxiliary spaces |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2511.06603 |