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Title: Reliable averaging for the primal variable in the Courant FEM and hierarchical error estimators on red-refined meshes
Authors: Carstensen, CarstenEigel, Martin
Issue Date: 2016
Published in: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik , Volume 2251, ISSN 2198-5855
Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Abstract: A hierarchical a posteriori error estimator for the first-order finite element method (FEM) on a red-refined triangular mesh is presented for the 2D Poisson model problem. Reliability and efficiency with some explicit constant is proved for triangulations with inner angles smaller than or equal to π/2 . The error estimator does not rely on any saturation assumption and is valid even in the pre-asymptotic regime on arbitrarily coarse meshes. The evaluation of the estimator is a simple post-processing of the piecewise linear FEM without any extra solve plus a higher-order approximation term. The results also allows the striking observation that arbitrary local averaging of the primal variable leads to a reliable and efficient error estimation. Several numerical experiments illustrate the performance of the proposed a posteriori error estimator for computational benchmarks.
Keywords: A posteriori; error analysis; finite element method; averaging; smoothing; hierarchical estimator; adaptivity; mesh refinement; convergence
DDC: 510
License: This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.
Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.
Appears in Collections:Mathematik

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