  In this work, we present numerical studies of fixed-stress iterative coupling
for solving flow and geomechanics with propagating fractures in a porous
medium. Specifically, fracture propagations are described by employing a
phase-field approach. The extension to fixed-stress splitting to propagating
phase-field fractures and systematic investigation of its properties are
important enhancements to existing studies. Moreover, we provide an accurate
computation of the fracture opening using level-set approaches and a subsequent
finite element interpolation of the width. The latter enters as fracture
permeability into the pressure diffraction problem which is crucial for fluid
filled fractures. Our developments are substantiated with several numerical
tests that include comparisons of computational cost for iterative coupling and
nonlinear and linear iterations as well as convergence studies in space and
time.
