Stabilized mixed hp-BEM for frictional contact problems in linear elasticity

TL;DR

This paper develops a stabilized mixed boundary element method for frictional contact problems in linear elasticity, ensuring convergence and providing error estimates, with numerical validation for Tresca and Coulomb friction.

Contribution

It introduces an hp-stabilization approach for boundary element methods applied to contact problems, addressing convergence issues in natural discretizations.

Findings

Proven convergence of the stabilized method for unilateral frictional contact problems.

Derived a priori and a posteriori error estimates for Tresca friction.

Numerical experiments confirm theoretical error bounds and effectiveness.

Abstract

We investigate hp-stabilization for variational inequalities and boundary element methods based on the approach introduced by Barbosa and Hughes for finite elements. Convergence of a stabilized mixed boundary element method is shown for unilateral frictional contact problems for the Lame equation. Without stabilization, this may not converge because the inf-sup constant need not be bounded away from zero for natural discretizations, even for fixed h and p. Both a priori and a posteriori error estimates are presented in the case of Tresca friction, for discretizations based on Bernstein or Gauss-Lobatto-Lagrange polynomials as test and trial functions. We also consider an extension of the a posteriori estimate to Coulomb friction. Numerical experiments underline our theoretical results.