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2001-29

Upper and Lower A Posteriori Error Estimates with Post-Processing for Nonconforming Finite Elements

by Schieweck, F..


Series: 2001-29, Preprints

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

Abstract:
For a nonconforming finite element approximation of an elliptic model
problem, we propose a posteriori error estimates in the energy norm
which use as an additive term the 'post-processing error' between
the original nonconforming finite element solution and an easy
computable conforming approximation of that solution.
Thus, for the error analysis, the existing theory from the conforming
case can be used together with some simple additional arguments.
As an essential point, the property is exploited that the nonconforming
finite element space contains as a subspace a conforming finite element
space of first order. This property is fulfilled for many known
nonconforming spaces.
We prove local lower and global upper a posteriori error estimates for
an enhanced error measure which is the discretization error in the
discrete energy norm plus the error of the best representation of the
exact solution by a function in the conforming space used for the
post-processing.
We demonstrate that the idea to use a computed conforming approximation of
the nonconforming solution can be applied also to derive an a posteriori
error estimate for a linear functional of the solution which represents
some quantity of physical interest.

Keywords:
a posteriori error estimates, nonconforming finite elements, post-processing