Duality based error control for the Signorini problem
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917627407892480 |
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| author | Ashby, Ben S. Pryer, Tristan |
| author_facet | Ashby, Ben S. Pryer, Tristan |
| contents | In this paper we study the a posteriori bounds for a conforming piecewise linear finite element approximation of the Signorini problem. We prove new rigorous a posteriori estimates of residual type in $L^{p}$, for $p \in (4,\infty)$ in two spatial dimensions. This new analysis treats the positive and negative parts of the discretisation error separately, requiring a novel sign- and bound-preserving interpolant, which is shown to have optimal approximation properties. The estimates rely on the sharp dual stability results on the problem in $W^{2,(4 - \varepsilon)/3}$ for any $\varepsilon \ll 1$. We summarise extensive numerical experiments aimed at testing the robustness of the estimator to validate the theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_01251 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Duality based error control for the Signorini problem Ashby, Ben S. Pryer, Tristan Numerical Analysis In this paper we study the a posteriori bounds for a conforming piecewise linear finite element approximation of the Signorini problem. We prove new rigorous a posteriori estimates of residual type in $L^{p}$, for $p \in (4,\infty)$ in two spatial dimensions. This new analysis treats the positive and negative parts of the discretisation error separately, requiring a novel sign- and bound-preserving interpolant, which is shown to have optimal approximation properties. The estimates rely on the sharp dual stability results on the problem in $W^{2,(4 - \varepsilon)/3}$ for any $\varepsilon \ll 1$. We summarise extensive numerical experiments aimed at testing the robustness of the estimator to validate the theory. |
| title | Duality based error control for the Signorini problem |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2404.01251 |