A finite element analysis for the Signorini problem in plane elastostatics

Abstract

The Signorini unilateral boundary value problem describes the equilibrium of an elastic body resting on a rigid and frictionless support. A displacement finite element method, using piecewise linear polynomials on the triangulation, can be applied to obtain an approximate solution. Assuming that the solution is sufficiently regular, the optimal rate of convergence is proved. Moreover, the convergence is justified even without any regularity assumption.