Summary
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 |α|≦1 an approximationu −α h (z) toD α u(z) with |D α u(z)−u −αh (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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Louis, A. Acceleration of convergence for finite element solutions of the Poisson equation. Numer. Math. 33, 43–53 (1979). https://doi.org/10.1007/BF01396494
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DOI: https://doi.org/10.1007/BF01396494