Local error bounds for post-processed finite element calculations

In this paper we produce tight guaranteed bounds for the error in the pointwise values of the derivatives of a post-processed nite element solution to a potential ow problem, in which the boundary condition is purely normal velocity. Our approach has to be modi ed for the problems with Dirichlet boundary conditions. The aim is to produce a tight envelope of certainty within which the exact value is guaranteed to lie. Our numerical experiments produce narrow envelopes at interior points and at points close to or on the boundary