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It does sound reasonable. The callback from PETSc does not work as I expected.
This is always called before the solve, so moving the two calls within the FEProblemSolve.C routine did not change the execution order.

I ll take a quick look to see if there are other options. You could hack post-NONLINEAR with the NONLINEAR_CONVERGENCE execute_on. But you would need petsc to declare the solve converged (with loose tolerances) and a MOOSE Convergence object to keep iterating. So pretty hacky

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