Nonlinear Iterative Operator-Splitting Methods and Applications for Nonlinear Parabolic Partial Differential Equations

In this paper we concentrate on nonlinear iterative operator splitting methods for nonlinear differential equations. The motivation arose from decoupling nonlinear operator equations in simpler operator equations. The decomposition in simpler equations allow to apply adaptive time-discretisation methods in each underlying time-scale. Therefore one can solve the equations more effectively and accurate. The underlying coupling of the splitting method is fulfilled with a relaxation, coming from the results of the previous time-steps, the adapted problems. We consider the consistency and stability analysis of the nonlinear iterative operator splitting method. The consistency analysis is based on linearisation. An a priori error estimates is derived for the linearised case. Finally we discuss the iterative operator-splitting methods for the applications to multi-physics problems