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A simple equilibration procedure leading to polynomial-degree-robust a posteriori error estimators for the curl-curl problem

Abstract : We introduce two a posteriori error estimators for Nédélec finite element discretizations of the curl-curl problem. These estimators pertain to a new Prager-Synge identity and an associated equilibration procedure. They are reliable and efficient, and the error estimates are polynomial-degree-robust. In addition, when the domain is convex, the reliability constants are fully computable. The proposed error estimators are also cheap and easy to implement, as they are computed by solving divergence-constrained minimization problems over edge patches. Numerical examples highlight our key findings, and show that both estimators are suited to drive adaptive refinement algorithms. Besides, these examples seem to indicate that guaranteed upper bounds can be achieved even in non-convex domains.
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Preprints, Working Papers, ...
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https://hal.inria.fr/hal-03323859
Contributor : Théophile Chaumont-Frelet Connect in order to contact the contributor
Submitted on : Monday, August 23, 2021 - 11:47:06 AM
Last modification on : Thursday, August 4, 2022 - 5:00:05 PM
Long-term archiving on: : Wednesday, November 24, 2021 - 6:11:35 PM

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chaumontfrelet_2021a.pdf
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  • HAL Id : hal-03323859, version 1
  • ARXIV : 2108.07552

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Théophile Chaumont-Frelet. A simple equilibration procedure leading to polynomial-degree-robust a posteriori error estimators for the curl-curl problem. 2021. ⟨hal-03323859⟩

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