In this thesis, we couple such algorithms with nonlinear Schwarz domain decomposition techniques. With this approach, we can develop efficient parallel adaptive wavelet Schwarz methods for a class of nonlinear problems and prove their convergence and optimality. We support the theoretical findings with instructive numerical experiments.
In addition, we present how these techniques can be applied to the stationary, incompressible Navier-Stokes equation. Furthermore, we couple the adaptive wavelet Schwarz methods with a Newton-type method.