One- and Two-Level Domain Decomposition Methods for Nonlinear Problems

In this paper we synthesize the results in [1] - [6] concerning the convergence rate of the one- and two-level methods for some nonlinear problems: nonlinear variational inequalities, inequalities with contraction operators, variational inequalities of the second kind and quasi-variational inequalities. Also, we verify that the convergence rates obtained by numerical tests are really in concordance with the theoretical ones. We comparatively illustrate the convergence rates of the one- and two-level methods by numerical experiments for the solution of the two-obstacle problem of a nonlinear elastic membrane.