  This work unifies pseudo-time and inexact regularization techniques for
nonmonotone classes of partial differential equations, into a regularized
pseudo-time framework. Convergence of the residual at the predicted rate is
investigated through the idea of controlling the linearization error, and
regularization parameters are defined following this analysis, then assembled
in an adaptive algorithm. The main innovations of this paper include the
introduction of a Picard-like regularization term scaled by its cancellation
effect on the linearization error to stabilize the Newton-like iteration; an
updated analysis of the regularization parameters in terms of minimizing an
appropriate quantity; and, strategies to accelerate the algorithm into the
asymptotic regime. Numerical experiments demonstrate the method on an
anisotropic diffusion problem where the Jacobian is not continuously
differentiable, and a model problem with steep gradients and a thin diffusion
layer.
