dolfin team mailing list archive

[Anders Logg <logg@xxxxxxxxx>]

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.

--
Anders

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