The Kačanov method for some nonlinear problems Original Research Article

The Kačanov method is an iteration method for solving some nonlinear partial differential equation problems. In each iteration, a linear problem is solved. In this paper, we discuss the use of the Kačanov method in the context of two model problems. We show the convergence of the Kačanov iteration sequences, and derive a posteriori error estimates for the Kačanov iterates. Numerical examples are given showing the convergence of the method and the effectiveness of the a posteriori error estimates.