  In this work, we extend a phase-field approach for pressurized fractures to
non-isothermal settings. Specifically, the pressure and the temperature are
given quantities and the emphasis is on the correct modeling of the interface
laws between a porous medium and the fracture. The resulting model is augmented
with thermodynamical arguments and then analyzed from a mechanical perspective.
The numerical solution is based on a robust semi-smooth Newton approach in
which the linear equation systems are solved with a generalized minimal
residual method and algebraic multigrid preconditioning. The proposed modeling
and algorithmic developments are substantiated with different examples in two-
and three dimensions. We notice that for some of these configurations
manufactured solutions can be constructed, allowing for a careful verification
of our implementation. Furthermore, crack-oriented predictor-corrector
adaptivity and a parallel implementation are used to keep the computational
cost reasonable. Snapshots of iteration numbers show an excellent performance
of the nonlinear and linear solution algorithms. Lastly, for some tests, a
computational analysis of the effects of strain-energy splitting is performed,
which has not been undertaken to date for similar phase-field settings
involving pressure, fluids or non-isothermal effects.
