The coming back to the original problem, I’m still unsure of how to diagnose 
the problem.  

I am not sure if the listserv supports image attachments, but I dumped the 
snes_check_jacobian_view to disk and inspected the matrices with the spy 
command. I find that no entry in the saved matrix has absolute value larger 
than 10^{-2}.  There are some that have absolute value larger than 10^{-3}, but 
the actual values of the entries at those indices are on the order of 100 or 
1000, meaning that they are small in a relative sense.

-gideon

> On Sep 9, 2015, at 12:19 PM, Jed Brown <[email protected]> wrote:
> 
> Gideon Simpson <[email protected]> writes:
> 
>> Checking the Jacobian, this is a pretty standard output:
>> 
>>      Testing hand-coded Jacobian, if the ratio is O(1.e-8), the hand-coded 
>> Jacobian is probably correct.
>>    Finite difference Jacobian
>>    Hand-coded Jacobian
>>    Hand-coded minus finite difference Jacobian
>>    6.08281e-10 = ||J - Jfd||//J|| 0.000151055  = ||J - Jfd||
>> 
>> 
>> Things look favorable in terms of relative difference, but the absolute 
>> difference is a bit more suspect.
> 
> It likely just means you have big matrix entries (perhaps due to poor 
> nondimensionalization/scaling).

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