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

摘要

Abstract 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 udocumentclass[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 uhdocumentclass[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.