fiat team mailing list archive

[Anders Logg <logg@xxxxxxxxx>]

On Tue, Dec 11, 2007 at 05:16:21PM +0100, Marie Rognes wrote:
> Robert Kirby wrote:
> > L2 projection into the finite element space.  On each element, or 
> > globally, solve
> > ( pi u - u , w ) = 0 for a function pi u for all of the test functions 
> > in the finite element space.
> >
> > All you need is point evaluation on the input function u for 
> > quadrature, and the weighted values of u become the rhs of the system.
> >
> > We could include the function value being integrated against, but it's 
> > going to be inexact.  I see creating interpolants as quite a bit of 
> > work with little payback when the infrastructure to do projection is 
> > already in place and typically is what is required by theorems anyway 
> > ( e.g. project initial conditions for parabolic problems into FE space).
> 
> But say that you want to enforce essential boundary conditions on your 
> spaces through replacing the equations in the linear system with the 
> values of the degrees of freedom on the boundary.  Then you would need 
> to know how to evaluate the degrees of freedom, right...?

I think so. For right-hand sides, we could do quadrature as suggested
or we could first evaluate the Lagrange nodes and then do a linear
transform from the Lagrange coefficients to say the BDM coefficients.

But for boundary conditions, we only know the trace of some given
function. Then I don't see how to do either projection (quadrature) or
evaluating Lagrange nodes and then projection. But direct evaluation
of the functionals (like computing the normal component at a point)
would work.

-- 
Anders