Ivan I. Dyyak

Ihor I. Prokopyshyn, Ivan I. Dyyak, Rostyslav M. Martynyak et al.

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.

Ivan I. Dyyak, Ihor I. Prokopyshyn, Ivan A. Prokopyshyn

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.

Ihor I. Prokopyshyn, Ivan I. Dyyak, Rostyslav M. Martynyak et al.

In this paper we propose on continuous level several domain decomposition methods to solve unilateral and ideal multibody contact problems of nonlinear elasticity. We also present theorems about convergence of these methods.