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

by Schieweck, F..

Series: 2000-11, Preprints

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

For a nonconforming finite element approximation of an elliptic model
problem, we propose an a posteriori error estimate in the energy norm
which uses 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 for 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.
For the a posteriori error bound, we prove that it has the same
asymptotic behavior as the energy norm of the real discretization
error itself.
We show that the ''post-processing error'' can be used also as an
additional error indicator.
Besides the error estimates in the global energy norm,
we demonstrate that the concept of using a conforming approximation of
the nonconforming solution can be applied also to derive an a posteriori
error estimate for linear functionals of the solution which represent
some quantities of physical interest.

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