  Models for multiphysics problems often contain strong nonlinearities.
Including fracture contact mechanics introduces discontinuities at the
transition between open and closed or sliding and sticking fractures. The
resulting system of equations is highly challenging to solve. The na\"ive
choice of Newton's method frequently fails to converge, calling for more
refined solution techniques such as line search methods. When dealing with
strong nonlinearities and discontinuities, a global line search based on the
magnitude of the residual of all equations is at best costly to evaluate and at
worst fails to converge. We therefore suggest a cheap and reliable approach
tailored to the discontinuities. Utilising adaptive variable scaling, the
algorithm uses a line search to identify the transition between contact states.
Then, a solution update weight is chosen to ensure that no fracture cells move
too far beyond the transition. We demonstrate the algorithm on a series of test
cases for poromechanics and thermoporomechanics in fractured porous media. We
consider both single- and multifracture cases and study the importance of
proper scaling of variables and equations.
