fiat team mailing list archive

[Marie Rognes <meg@xxxxxxxxxxx>]

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...?

--
Marie E. Rognes
Ph.D Fellow, 
Centre of Mathematics for Applications, 
University of Oslo
http://folk.uio.no/meg