Domain decomposition method for a model crack problem with a possible contact of crack edges

The scalar Poisson equation is considered in a domain having a cut with unilateral constraints specified on its edges. An iterative method is proposed for solving the problem. The method is based on domain decomposition and the Uzawa algorithm for finding a saddle point of the Lagrangian. According to the method, the original domain is divided into two subdomains and a linear problem for Poisson’s equation is solved in each of them at every iteration step. The solution in one domain is related to that in the other by two Lagrange multipliers: one is used to match the solutions, and the other, to satisfy the unilateral constraint. Examples of the numerical solution of the problem are given.