Adaptive FE-BE Coupling for Strongly Nonlinear Transmission Problems with Coulomb Friction

TL;DR

This paper presents an adaptive finite element/boundary element method for nonlinear elastoplastic interface problems with Coulomb friction, demonstrating convergence to the unique solution using variational inequalities and saddle point formulations.

Contribution

It introduces a novel adaptive coupling approach for strongly nonlinear transmission problems involving friction, with proven convergence of the Galerkin approximations.

Findings

Convergence of Galerkin approximations to the unique solution.

Effective adaptive mesh refinement based on gradient recovery.

Successful application to elastoplastic interface problems with Coulomb friction.

Abstract

We analyze an adaptive finite element/boundary element procedure for scalar elastoplastic interface problems involving friction, where a nonlinear uniformly monotone operator such as the p-Laplacian is coupled to the linear Laplace equation on the exterior domain. The problem is reduced to a boundary/domain variational inequality, a discretized saddle point formulation of which is then solved using the Uzawa algorithm and adaptive mesh refinements based on a gradient recovery scheme. The Galerkin approximations are shown to converge to the unique solution of the variational problem in a suitable product of L^p- and L^2-Sobolev spaces.