Acceleration of convergence for finite element solutions of the Poisson equation |
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Authors: | Alfred Louis |
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Institution: | (1) Universität des Saarlandes, Angewandte Mathematik und Informatik, Fachbereich 10, 66 Saarbrücken, Germany (Fed. Rep.) |
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Abstract: | Summary Letu
h
be the finite element solution to–u=f with zero boundary conditions in a convex polyhedral domain . Fromu
h
we calculate for eachz 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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Keywords: | AMS (Mos): 65N30 CR: 5 17 |
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