Pointwise a Posteriori Error Analysis of a Finite Element Method for the Signorini Problem

In this article, we develop a posteriori error control of conforming finite element method in maximum norm for the one-body contact problem. The reliability and the efficiency of the error estimator is discussed. The upper and lower barriers of the exact solution u\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{u}}$$\end{document} have been constructed by rectifying the discrete solution uh\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{u}}_{{\varvec{h}}}$$\end{document} properly and they are crucially used in obtaining the reliability estimates. Other key ingredients of the analysis are the sign property of the quasi-discrete contact force density as well as bounds on the Green’s matrix of the divergence type operator. Numerical experiments are presented for a two dimensional contact problems that exhibit reliability and efficiency of the error estimator confirming theoretical findings.