Abstract
Letu h be the finite element solution to?Δu=f with zero boundary conditions in a convex polyhedral domain Ω. Fromu h we calculate for eachz?Ω and |?|?1 an approximationu h ?? (z) toD ? u(z) with |D ? u(z)?u h ?? (z)|=O(h 2k?2) wherek is the order of the finite elements. The same superconvergence order estimates are obtained also for the boundary flux. We need not work on a regular mesh but we have to compute averages ofu h where the diameter of the domain of integration must not depend onh.
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