$\textit{A priori}$ and $\textit{a posteriori}$ error identities for the scalar Signorini problem
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913431500619776 |
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| author | Bartels, Sören Gudi, Thirupathi Kaltenbach, Alex |
| author_facet | Bartels, Sören Gudi, Thirupathi Kaltenbach, Alex |
| contents | In this paper, on the basis of a (Fenchel) duality theory on the continuous level, we derive an $\textit{a posteriori}$ error identity for arbitrary conforming approximations of the primal formulation and the dual formulation of the scalar Signorini problem. In addition, on the basis of a (Fenchel) duality theory on the discrete level, we derive an $\textit{a priori}$ error identity that applies to the approximation of the primal formulation using the Crouzeix-Raviart element and to the approximation of the dual formulation using the Raviart-Thomas element, and leads to quasi-optimal error decay rates without imposing additional assumptions on the contact set and in arbitrary space dimensions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_10912 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $\textit{A priori}$ and $\textit{a posteriori}$ error identities for the scalar Signorini problem Bartels, Sören Gudi, Thirupathi Kaltenbach, Alex Numerical Analysis 35J20, 49J40, 49M29, 65N30, 65N15, 65N50 In this paper, on the basis of a (Fenchel) duality theory on the continuous level, we derive an $\textit{a posteriori}$ error identity for arbitrary conforming approximations of the primal formulation and the dual formulation of the scalar Signorini problem. In addition, on the basis of a (Fenchel) duality theory on the discrete level, we derive an $\textit{a priori}$ error identity that applies to the approximation of the primal formulation using the Crouzeix-Raviart element and to the approximation of the dual formulation using the Raviart-Thomas element, and leads to quasi-optimal error decay rates without imposing additional assumptions on the contact set and in arbitrary space dimensions. |
| title | $\textit{A priori}$ and $\textit{a posteriori}$ error identities for the scalar Signorini problem |
| topic | Numerical Analysis 35J20, 49J40, 49M29, 65N30, 65N15, 65N50 |
| url | https://arxiv.org/abs/2407.10912 |