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A new Flyspray task has been opened.  Details are below. 

User who did this - Kilian Weishaupt (Kilian) 

Attached to Project - DuMuX
Summary - Automatically save restart file before simulation breaks down
Task Type - Feature Request
Category - General
Status - New
Assigned To - Kilian Weishaupt
Operating System - Unspecified
Severity - Low
Priority - Normal
Reported Version - Git
Due in Version - 2.9
Due Date - Undecided
Details - What do you think about creating a restart file just before the 
simulation stops when the maximum number of time step divisions has been 
reached?

So one could manually change some settings for the solver or set a different 
timestep size and resume from the very last point before the simulation ended.

My idea would be to include this in the timeIntegration() function:

....
        serialize();
        DUNE_THROW(Dune::MathError,
                   "Newton solver didn't converge after "
                   << maxFails
                   << " time-step divisions. dt="
                   << this->timeManager().timeStepSize()
                   << ". The solution of the last time step "
                   << "has been saved to a restart file.");
.....

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http://www.dumux.org/flyspray/index.php?do=details&task_id=307

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