• Journal of the Korean Mathematical Society
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• v.52 no.5
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• pp.891-906
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• 2015

In this work we analyze a postprocessing scheme for improving the guaranteed error bound based on the equilibrated fluxes for the P1 conforming FEM. The improved error bound is shown to be asymptotically exact under suitable conditions on the triangulations and the regularity of the true solution. We also present some numerical results to illustrate the effect of the postprocessing scheme.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.27 no.4
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• pp.245-271
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• 2023

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.