dolfin team mailing list archive

[Anders Logg <logg@xxxxxxxxx>]

This is now implemented. Watch out for the messages printed by FFC
during compilation:

  Adjusting element degree from ? to 3

Let me know you spot any cases where the degree selection does not
make sense.

Note that quadrature and tensor representation use different ways to
estimate the degree. For tensor representation, coefficients are
always interpolated so the integrand is always a polynomial.

Therefore, quadrature representation looks at the UFL function

  estimate_max_polynomial_degree

which now actually computes the maximum not degree (not the sum),
while tensor representation looks at the UFL function

  estimate_total_polynomial_degree

New versions of FFC and UFL needed.

--
Anders


On Mon, Nov 30, 2009 at 09:08:54PM +0100, 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 well 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.
>
> 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 that 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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