dolfin team mailing list archive

[Anders Logg <logg@xxxxxxxxx>]

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:
> >>>> noreply@xxxxxxxxxxxxx wrote:
> >>>>> ------------------------------------------------------------
> >>>>> revno: 4323
> >>>>> committer: Anders Logg <logg@xxxxxxxxx>
> >>>>> 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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