On Mon, Dec 2, 2013 at 3:06 PM, Jed Brown <[email protected]> wrote: > Geoffrey Irving <[email protected]> writes: >> I'm not sure what you mean by the weak form being symmetric, unless >> you mean that the primal and dual spaces are the same, which is just a >> restatement of my question (and therefore I'm not sure in the context >> of petsc). > > If my weak form is advection (\int v \cdot \nabla u) then I don't have a > useful energy. There are lots of things that could cause a stated > "energy" to be nonsense; matching basis functions is just one of them, > and perhaps not even the most common.
Yes, a routine to evaluate the energy only makes sense in contexts where the residuals are integrable/conservative. Obviously the user has to ensure this, possibly with the help of consistency checking routines (which I would write anyways if they aren't immediately available). >> The actual functional in the weak form PDE isn't symmetric except in >> special cases such as Poisson, but presumably that's not what you >> mean. Indefiniteness is somewhat inevitable (except near well behaved >> extreme solutions), and where it occurs depends on physics. > > That sort of indefiniteness doesn't make the energy meaningless, but add > a Lagrange multiplier and the Lagrangian is no longer an energy. Of course. In this case it would be useful as a consistency check but not as an objective to minimize. Geoffrey
