00-25

A General Transfer Operator for Arbitrary Finite Element Spaces

by Schieweck, F.

 

Preprint series: 00-25, 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 and conforming finite elements, interpolation operator,stability and error estimates, a posteriori error estimation,post-processing,multigrid prolongation


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