[petsc-users] Matrix-free vs finite differenced Jacobian approximation

[zakaryah .]

When you say "Jacobians are bad" and "debugging the Jacobians", do you mean
that the hand-coded Jacobian is wrong?  In that case, why would you be
surprised that the finite difference Jacobians, which are "correct" to
approximation error, perform better?  Otherwise, what does "Jacobians are
bad" mean - ill-conditioned?  Singular?  Not symmetric?  Not positive
definite?
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