by Schieweck, F..
Series: 2000-25, Preprints
We construct and analyze a transfer operator from any given
(e.g. nonconforming) to an arbitrary desired
(e.g. higher order conforming) finite element space.
This transfer operator also defines a stable interpolation
operator for element-wise smooth functions satisfying Dirichlet
boundary conditions. It can be generalized in a natural way for
The practical computation of the transfered function can be implemented
For the transfer operator, we prove local and global stability estimates
in the L^2-norm and the H^1-semi-norm.
Furthermore, we prove local and global error estimates between the exact
solution of some problem and the ``post-processed'' numerical solution
computed by the action of the transfer operator applied to the discrete
solution of the problem in the primary given finite element space.
As applications we discuss a posteriori error estimation,
graphical output and multigrid prolongation.