In the finite element analysis of elasticity and plasticity problems, we often require the FE grid which is locally refined to be able to catch a highly nonlinear behaviour of the exact solution in some parts of the problem domain. For this purpose, we can either refine the global FE grid or use composite grids consisting from a global coarse grid and local finer grids (patches). The later approach can be advantageously accompanied by iterative solution methods which include the solution of the global and local subproblems in each iteration.
This contribution is devoted to iterative methods and solvers of this type which are based on the alternating Schwarz algorithm. More precisely, we shall describe the fast adaptive composite grid method (FAC) and similar iterative procedures. We shall present some comparison of these methods and discussion of their convergence and some implementation aspects.