Search

We propose computable a posteriori error estimates for a second order nonconforming finite element approximation of the Stokes problem. The estimator is completely free of unknown constants and gives a guaranteed numerical upper bound on the error, in terms of a lower bound for the inf-sup constant of the underlying continuous problem. The estimator is also shown to provide a lower bound on the error up to a constant and higher order data oscillation terms. Numerical results are presented illustrating the theory and the performance of the estimator.

Fully computable, guaranteed bounds are obtained on the error in the finite element approximation which take the effect of the boundary approximation into account. We consider the case of piecewise affine approximation of the Poisson problem with pure Neumann boundary data, and obtain a fully computable quantity which is shown to provide a guaranteed upper bound on the energy norm of the error. The estimator provides, up to a constant and oscillation terms, local lower bounds on the energy norm of the error.