On the coupling of regularization techniques and the boundary element method for a hemivariational inequality modelling a delamination problem

TL;DR

This paper develops a method combining regularization of nonsmooth optimization with the boundary element method to effectively solve hemivariational inequalities in delamination contact problems, demonstrating convergence and providing error estimates.

Contribution

It introduces a novel coupling of regularization techniques with h-BEM for hemivariational inequalities, including convergence analysis and error estimation.

Findings

Proves convergence of the h-BEM Galerkin solution in the energy norm.

Provides an a-priori error estimate for the discretized problem.

Demonstrates the method with a numerical example.

Abstract

In this paper, we couple regularization techniques of nondifferentiable optimization with the h-version of the boundary element method (h-BEM) to solve nonsmooth variational problems arising in contact mechanics. As a model example we consider the delamination problem. The variational formulation of this problem leads to a hemivariational inequality (HVI)with a nonsmooth functional defined on the contact boundary. This problem is first regularized and then discretized by a h-BEM. We prove convergence of the h-BEM Galerkin solution of the regularized problem in the energy norm, provide an a-priori error estimate and give a numerical example.