Domain decomposition methods for problems of unilateral contact between elastic bodies with nonlinear Winkler covers

TL;DR

This paper introduces Robin-Robin domain decomposition methods for unilateral contact problems involving elastic bodies with nonlinear Winkler covers, supported by theoretical analysis and finite element numerical experiments.

Contribution

It develops a new class of domain decomposition algorithms for nonlinear unilateral contact problems with nonlinear Winkler covers, combining abstract iterative methods with finite element analysis.

Findings

Methods effectively solve nonlinear unilateral contact problems.

Numerical experiments demonstrate convergence and accuracy.

Approach extends existing domain decomposition techniques.

Abstract

In this paper we propose on continuous level a class of domain decomposition methods of Robin-Robin type to solve the problems of unilateral contact between elastic bodies with nonlinear Winkler covers. These methods are based on abstract nonstationary iterative algorithms for nonlinear variational equations in reflexive Banach spaces. We also provide numerical investigations of obtained methods using finite element approximations.