Journal of the Korean Society for Industrial and Applied Mathematics

Korean Society for Industrial and Applied Mathematics (한국산업응용수학회)
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SUPERCONVERGENCE AND POSTPROCESSING OF EQUILIBRATED FLUXES FOR QUADRATIC FINITE ELEMENTS

  • KWANG-YEON KIM (DEPARTMENT OF MATHEMATICS, KANGWON NATIONAL UNIVERSITY)
  • Received : 2023.10.30
  • Accepted : 2023.12.25
  • Published : 2023.12.25
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Abstract

In this paper we discuss some recovery of H(div)-conforming flux approximations from the equilibrated fluxes of Ainsworth and Oden for quadratic finite element methods of second-order elliptic problems. Combined with the hypercircle method of Prager and Synge, these flux approximations lead to a posteriori error estimators which provide guaranteed upper bounds on the numerical error. Furthermore, we prove some superconvergence results for the flux approximations and asymptotic exactness for the error estimator under proper conditions on the triangulation and the exact solution. The results extend those of the previous paper for linear finite element methods.

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References

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