Pseudo-Transient Continuation seems to be a robust way of globalizing Newton's method. It should be possible to implement this for general problems in cashocs.
One note: Users should have the option (optional!) to supply their own time derivative. This can be very useful when using mixed problems, where only one variable is truly time-dependent. This is analogous to the DAE formulation of Pseudo-Transient-Continuation.
Another possible implementation would be for the user to indicate which parts of the (mixed) solution should receive time-derivatives.
Pseudo-Transient Continuation seems to be a robust way of globalizing Newton's method. It should be possible to implement this for general problems in cashocs.
One note: Users should have the option (optional!) to supply their own time derivative. This can be very useful when using mixed problems, where only one variable is truly time-dependent. This is analogous to the DAE formulation of Pseudo-Transient-Continuation. Another possible implementation would be for the user to indicate which parts of the (mixed) solution should receive time-derivatives.