Duality based error control for the Signorini problem
<|reference_start|>Duality based error control for the Signorini problem: 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.<|reference_end|>
@article{ashby2024duality,
    title={Duality based error control for the Signorini problem},
    author={Ben S. Ashby and Tristan Pryer},
    journal={arXiv preprint arXiv:2404.01251},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.01251},
    primaryClass={math.NA cs.NA}
}