Domain decomposition method for contact problems with small range contact

A non-overlapping domain decomposition algorithm of Neumann–Neumann type for solving variational inequalities arising from the elliptic boundary value problems in two dimensions with unilateral boundary condition is presented. We suppose that boundary with inequality condition is ‘relatively’ small. First, the linear auxiliary problem, where the inequality condition is replaced by the equality condition, is solved. In the second step, the solution of the auxiliary problem is used in a successive approximations method. In these solvers, a preconditioned conjugate gradient method with Neumann–Neumann preconditioner is used for solving the interface problems, while local problems within each subdomain are solved by direct solvers. A convergence of the iterative method is proved and results of computational test are reported.