ffc team mailing list archive

[Anders Logg <logg@xxxxxxxxx>]

On Mon, Nov 30, 2009 at 11:01:59PM +0000, Garth N. Wells wrote:
>
>
> Anders Logg wrote:
> > We still haven't decided on the correct strategy for choosing the
> > degree of an unspecified element.
> >
> > What we have now looks at the total degree of the form and then sets
> > the degree accordingly. This doesn't really work weoull and the reason
> > is quite simple: We can't figure out the total degree correctly if we
> > don't know the degree of the coefficient.
> >
> > So my new suggestion is the following. We simply scan all elements in
> > the form with specified degrees and set the degree to the maximum
> > degree among the elements.
> >
>
> Or should it be the maximum degree of the test and trial functions?

Yes, that's basically what happens now. It looks at everything that
has a degree so it looks at the test and trial functions but also at
any coefficients that may happen to have a degree.

That's useful for say v*f*g*dx if one of f and g happen to have a
degree specified. Then the degree for the other needs to be the same.

> Do you take into accout derivatives, e.g. for
>
>   w*dot(grad(v), grad(u))*dx
>
> would w be of the same order as v and u, or one order lower?

Yes, derivatives are taken into account, but that's maybe not what we
want. In the above case, the results will be q = 1 for w coming from

  max((1, 0, 0))

The 1 comes from the default degree q = 1 used when estimating the
max degree for a form with an unknown coefficient.

Perhaps we should not look at derivatives at all when selecting the
quadrature degree?

--
Anders


> Garth
>
> > Here are some use cases:
> >
> > 1. v*f*dx
> >
> > If v is an element of degree q, then the degree for the approximation
> > of f is set to q.
> >
> > For quadrature elements, this means thatd we get a quadrature error in
> > the integral of order q + 1 which in many cases is the same as the
> > convergence of the finite element method.
> >
> > For Lagrange elements, we get an interpolation error when
> > approximating f of degree q + 1 so the situation is the same.
> >
> > 2. v*f*g*dx
> >
> > Same as above here if f and g have unspecified degrees. But if f or g
> > should happen to have a degree higher than q, than that degree will be
> > used for the other coefficient if unspecified.
> >
> > I'll go ahead and make this change in FFC. It's rather easy to change
> > the strategy and FFC is being very verbose about the choices it makes,
> > at least until we have settled on an acceptable strategy.
> >
>
>

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