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2000-25

A General Transfer Operator for Arbitrary Finite Element Spaces

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