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Pseudo-transient continuation solver for globalizing Newton's method
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.
Just a comment: This is already implemented with the PETSc TS module - maybe we can use this? This is in line with the discussion of #441
I'll close this issue as cashocs now has a interface for PETSc's SNES - this includes, e.g., trust region methods that can be used to globalize Newton's method.