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