$\textitA priori$ and $\textita posteriori$ error identities for the scalar Signorini problem
<|reference_start|>$\textitA priori$ and $\textita posteriori$ error identities for the scalar Signorini problem: 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.<|reference_end|>
@article{bartels2024$\textit{a,
    title={$\textit{A priori}$ and $\textit{a posteriori}$ error identities for the
  scalar Signorini problem},
    author={S"oren Bartels, Thirupathi Gudi and Alex Kaltenbach},
    journal={arXiv preprint arXiv:2407.10912},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.10912},
    primaryClass={math.NA cs.NA}
}