by Schieweck, F..

**Series:** 2000-11, 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 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.

**Keywords:**

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