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18 February 2025
 
  » arxiv » 1508.0191

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Improved ZZ A Posteriori Error Estimators for Diffusion Problems: Conforming Linear Elements
Zhiqiang Cai ; Shun Zhang ;
Date 2 Aug 2015
AbstractFor non-smooth problems, e.g., interface problems, it is known that adaptive mesh refinement (AMR) algorithms using the Zienkiewicz-Zhu (ZZ) a posteriori error estimator are not efficient to reduce global error. In this paper, we derive and analyze two improved ZZ error estimators for the conforming linear finite element approximation to the diffusion problem with full coefficient tensor. The estimators are based on the piecewise "constant" and linear flux recoveries in the $H(div;Omega)$ conforming finite element spaces. Both the recoveries are explicit. When the diffusion coefficient is piecewise constant scalar and its distribution is locally quasi-monotone, it is shown theoretically that the estimators developed in this paper are robust with respect to the size of jumps. Numerical experiments are also performed to support the theoretical results.
Source arXiv, 1508.0191
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