On Thu, Nov 26, 2009 at 11:16:35PM +0000, Garth N. Wells wrote: > > > Anders Logg wrote: > > On Thu, Nov 26, 2009 at 11:07:20PM +0000, Garth N. Wells wrote: > >> > >> Anders Logg wrote: > >>> On Thu, Nov 26, 2009 at 10:55:14PM +0000, Garth N. Wells wrote: > >>>> [email protected] wrote: > >>>>> ------------------------------------------------------------ > >>>>> revno: 4323 > >>>>> committer: Anders Logg <[email protected]> > >>>>> branch nick: dolfin-dev > >>>>> timestamp: Thu 2009-11-26 11:15:01 +0100 > >>>>> message: > >>>>> Use Lagrange as default element instead of quadrature for expressions. > >>>> I thought that we agreed that this is a bad idea. > >>>> > >>>> Garth > >>> I don't see why it is such a bad idea. Either we approximate a > >>> coefficient by interpolating it into a finite element space or we > >>> evaluate it at quadrature points. Just two different approaches to > >>> approximation. > >>> > >> We discussed this a few days ago and agreed that it's not good. > > > > I don't remember why I agreed really. I keep getting back to thinking > > it's not that bad. :-) > > > >> How should the order be chosen? > > > > The order can be chosen to preserve the order of approximation, for > > which it is enough to take the degree to be the same as that for the > > test and trial functions. > > > > This is what we do in bench/fem/convergence which shows the expected > > convergence rates for degree 1-5 (but I haven't checked in a while). > > > >> All the finite element codes that > >> I'm aware of would evaluate an Expression at quadrature points, so > >> that's what most users would expect. > > > > DOLFIN has been interpolating to a FEM space for the last 5 years and > > that has worked fine... :-) > > > > Why did we add QuadratureElements then?
I thought it was because you found that the quadratic convergence i Newton was destroyed for certain applications. > It's not just a question of what works, it's what would one expect. We should do what works best, not what's expected. I do agree that quadrature works just as well for coefficients as interpolation and better in some cases (like getting the quadratic convergence) so it should be the default. But I don't agree that interpolation is evil. It's just another option that might be preferred in some cases. -- Anders
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