Convergence of penalty Robin-Robin domain decomposition methods for unilateral multibody contact problems of elasticity

TL;DR

This paper introduces and mathematically justifies penalty Robin-Robin domain decomposition methods for solving unilateral multibody contact problems in elasticity, demonstrating their convergence and numerical efficiency.

Contribution

The paper provides the first rigorous convergence proofs for penalty Robin-Robin DDMs applied to unilateral contact problems in elasticity.

Findings

Proved convergence theorems for the proposed DDMs.

Validated numerical efficiency through finite element simulations.

Abstract

The paper is devoted to the penalty Robin-Robin domain decomposition methods (DDMs), proposed by us for the solution of unilateral multibody contact problems of elasticity. These DDMs are based on the penalty method for variational inequalities and some stationary and nonstationary iterative methods for nonlinear variational equations. The main result of the paper is that we give the mathematical justification of proposed DDMs and prove theorems on their convergence. We also investigate the numerical efficiency of these methods using the finite element approximations.