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Article overview
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Improved ZZ A Posteriori Error Estimators for Diffusion Problems: Conforming Linear Elements | Zhiqiang Cai
; Shun Zhang
; | Date: |
2 Aug 2015 | Abstract: | For 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 | Services: | Forum | Review | PDF | Favorites |
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