Error Analysis of a Frictional Piezoelectric Contact Problem

Abstract

In this work, a particular class of penalized Signorini’s models with a normal compliance contact condition is studied. These contact models are created by taking two parameters: a power parameter \(\alpha \geq 1\) and a punishment parameter \(\varepsilon \). A standard penalization is represented by a value of \(\alpha =1\). These contact models function as nonlinear approximations for Signorini’s problem. Choosing a continuous, conforming linear finite element approximation is the first step in our method. We then calculate \(L^{2}\)-error estimates with suitable assumptions, which are carefully examined and explained.