fiat team mailing list archive

[Anders Logg <logg@xxxxxxxxx>]

On Mon, Dec 10, 2007 at 06:47:27PM -0600, Robert Kirby wrote:
> 1.) This is ill-posed, in general.  You can't integrate a generic function just
> by using it as a black-box.  This handles Lagrange interpolation, but not
> Raviart-Thomas, which has integral moments against some functions as some of
> the nodes.

Can't we just include the value of the function we integrate against
in the weights?

> 2.) Why don't you do L2 projection instead?  Generally, you get a mass matrix
> that is so much cheaper to solve than anything else you're doing that it
> doesn't cost very much.  Everything is already in place for that.

L2 projection between which spaces? What we want to do is to
interpolate (evaluate the dofs) locally on each element. We don't
solve a global system.

-- 
Anders


> 
> 
> 
> On Dec 10, 2007 1:51 PM, Anders Logg <logg@xxxxxxxxx> wrote:
> 
>     On Mon, Dec 10, 2007 at 09:08:33AM -0600, Robert Kirby wrote:
>     > By "given function", do you mean an arbitrary input function (something
>     that
>     > supports __call__) or something in the finite element space?
> 
>     A function that can be evaluated at any point. For example, someone
>     has specified a right-hand side by "return sin(x)".
> 
> 
> 
>     > Functionals know how to apply themselves to the finite-dimensional space
>     > members via __call__ (it's just a dot product).
>     >
>     > There is some preliminary support for the types of functionals in the
>     "get_type
>     > ()" method.  It would need to be expanded to include some of this other
>     > information.
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