Matthew Knepley <knep...@gmail.com> writes: > On Wed, Oct 11, 2023 at 1:03 PM Jed Brown <j...@jedbrown.org> wrote: > >> I don't see an attachment, but his thesis used conservative variables and >> defined an effective length scale in a way that seemed to assume constant >> shape function gradients. I'm not aware of systematic literature comparing >> the covariant and contravariant length measures on anisotropic meshes, but >> I believe most people working in the Shakib/Hughes approach use the >> covariant measure. Our docs have a brief discussion of this choice. >> >> https://libceed.org/en/latest/examples/fluids/#equation-eq-peclet >> >> Matt, I don't understand how the second derivative comes into play as a >> length measure on anistropic meshes -- the second derivatives can be >> uniformly zero and yet you still need a length measure. >> > > I was talking about the usual SUPG where we just penalize the true residual.
I think you're focused on computing the strong diffusive flux (which can be done using second derivatives or by a projection; the latter produces somewhat better results). But you still need a length scale and that's most naturally computed using the derivative of reference coordinates with respect to physical (or equivalently, the associated metric tensor).
