  We consider a phase-field fracture propagation model, which consists of two
(nonlinear) coupled partial differential equations. The first equation
describes the displacement evolution, and the second is a smoothed indicator
variable, describing the crack position. We propose an iterative scheme, the
so-called $L$-scheme, with a dynamic update of the stabilization parameters
during the iterations. Our algorithmic improvements are substantiated with two
numerical tests. The dynamic adjustments of the stabilization parameters lead
to a significant reduction of iteration numbers in comparison to constant
stabilization values.
