Abstract
We present a patch-based equilibrated flux recovery procedure for the conforming finite element approximation to diffusion problems. The recovered flux is computed as the solution to a local constraint-free minimization problem on each patch. The approach is valid for higher order conforming elements in both two and three dimensions. The resulting estimator admits guaranteed reliability and the robust local efficiency is proved under the quasi-monotonicity condition of the diffusion coefficient. Numerical experiments are given to confirm the theoretical results.
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Zhiqiang Cai: This work was supported in part by the National Science Foundation under Grant DMS-1522707. Shun Zhang: This work was supported in part by Hong Kong Research Grants Council under the GRF Grant Project No. 11305319, CityU 9042090.
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Cai, D., Cai, Z. & Zhang, S. Robust equilibrated a posteriori error estimator for higher order finite element approximations to diffusion problems. Numer. Math. 144, 1–21 (2020). https://doi.org/10.1007/s00211-019-01075-1
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DOI: https://doi.org/10.1007/s00211-019-01075-1