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The output files only get written to when the run completes; to get around this, redirect the output to a file. So the line in the moab script that runs a program looks like this:
mpirun -np $nproc -machinefile $PBS_NODEFILE ./elemental > output.txt
This only redirects the output, not the error messages; if you want both you'd put 2>&1 at the end of the line.