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. > 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.
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