Abstract
In this paper, a contraction property is proved for an adaptive finite element method for controlling the global L 2 error on convex polyhedral domains. Furthermore, it is shown that the method converges in L 2 with the best possible rate. The method that is analyzed is the standard adaptive method except that, if necessary, additional refinements are made to keep the meshes sufficiently mildly graded. This modification does not compromise the quasi-optimality of the resulting algorithm.
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A. Demlow was partially supported by National Science Foundation Grant DMS-0713770.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Demlow, A., Stevenson, R. Convergence and quasi-optimality of an adaptive finite element method for controlling L 2 errors. Numer. Math. 117, 185–218 (2011). https://doi.org/10.1007/s00211-010-0349-9
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DOI: https://doi.org/10.1007/s00211-010-0349-9