dolfin team mailing list archive

["Garth N. Wells" <gnw20@xxxxxxxxx>]

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?

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?

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.
> 
> --
> Anders
> 
> 
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