Are you thinking about this PR again?

https://bitbucket.org/petsc/petsc/pull-requests/506

There's an issue here that Krylov methods operate in the discrete inner
product while some higher level operations are of interest in
(approximations of) continuous inner products (or norms).  The object in
PETSc that endows continuous attributes (like a hierarchy, subdomains,
fields) on discrete quantities is DM, so my first inclination is that
any continuous interpretation of vectors, including inner products and
norms, belongs in DM.

"Munson, Todd" <tmun...@mcs.anl.gov> writes:

> There is a bit of code in TAO that allows the user to change the norm to 
> a matrix norm.  This was introduced to get some mesh independent 
> behavior in one example (tao/examples/tutorials/ex3.c).  That 
> norm, however, does not propagate down into the KSP methods
> and is only used for testing convergence of the nonlinear
> problem.
>
> A few questions then:  Is similar functionality needed in SNES?  Are 
> TAO and SNES even the right place for this functionality?  Should 
> it belong to the Vector class so that you can change the inner 
> products and have all the KSP methods (hopefully) work 
> correctly?
>
> Note: that this discussion brings us to the brink of supporting an 
> optimize-then-discretize approach.  I am not convinced we should 
> go down that rabbit hole.
>
> Thanks, Todd.

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