Numerical solution of elliptic boundary problems on composite grid

Numerical domain decomposition algorithms for elliptic boundary value problem solution in two-dimensional complex domain with overlapping subdomains are derived. Boundary fitted grid is created in subdomain near boundary, but ordinary one is used in other subdomain. Accuracy estimates of numerical solution on composite grid are obtained when solution compatibility is implemented by means of some variants of classical alternating Swartz method. Numerical results are presented for model problem.