ffc team mailing list archive

[Anders Logg <logg@xxxxxxxxx>]

On Mon, Nov 23, 2009 at 07:39:24AM +0100, Kristian Oelgaard wrote:
> Quoting Anders Logg <logg@xxxxxxxxx>:
>
> > On Tue, Nov 17, 2009 at 09:28:23PM +0000, Garth N. Wells wrote:
> > >
> > >
> > > Anders Logg wrote:
> > > >I've added support in UFL and FFC for letting quadrature degree be
> > > >None for a quadrature element.
> > > >
> > > >This lets the form compiler choose the quadrature. What currently
> > > >happens is that the degree is counted as 1
> > >
> > > Polynomial degree or 'quadrature degree' (whatever that is)?
> > >
> > > (default value controllable
> > > >from the form compiler) and the summed with other functions
> > > >multiplying the coefficient.
> > > >
> > > >  L = v*f*dx
> > > >
> > > >If v is P2, then the total degree will be 2 + 1 = 3, which means the
> > > >quadrature degree chosen by FFC is 3 for that integral and so also
> > > >for the element for f.
>
> Sounds reasonable.
>
> > > >Then there seems to be some confusion about the difference between
> > > >quadrature order and degree. At least I'm confused.
> > >
> > > Me too.
>
> It should be the same thing, but we could sort out the naming to avoid
> confusion. I think this originates from Martin using 'polynomial degree' and I
> used 'polynomial order' when first implementing this.

I think degree is better. Quadrature order q can mean either that the error
converges as h^q and polynomials of degree q - 1 are integrated
exactly, or it can (in the case of Gauss quadrature) that it
integrates polynomials of degree 2q - 1 exactly.

We can define degree of a quadrature rule to be the polynomial degree
it integrates exactly. Then there's no confusion.

The problem is the following though. Should the quadrature rule of an
element be an appropriate rule for the entire integrand, or should it
be the polynomial degree approximation of the coefficient?

Currently, if one has w being defined on a quadrature element of
degree q, then the form

  w^n * dx

gets a total degree of n * q and FFC adjusts the quadrature rule to
that total degree.

--
Anders

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