by Schieweck, F..

**Series:** 2000-25, Preprints

- MSC:
- 65N15 Error bounds
- 65N30 Finite elements, ~Rayleigh-Ritz and Galerkin methods, finite methods
- 65D05 Interpolation

**Abstract:**

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

rough L^1-functions.

The practical computation of the transfered function can be implemented

efficiently.

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.

**Keywords:**

nonconforming