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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