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p-robust equilibrated flux reconstruction in H(curl) based on local minimizations. Application to a posteriori analysis of the curl-curl problem

Abstract : We present a local construction of H(curl)-conforming piecewise polynomials satisfying a prescribed curl constraint. We start from a piecewise polynomial not contained in the H(curl) space but satisfying a suitable orthogonality property. The procedure employs minimizations in vertex patches and the outcome is, up to a generic constant independent of the underlying polynomial degree, as accurate as the best-approximations over the entire local versions of H(curl). This allows to design guaranteed, fully computable, constant-free, and polynomial-degree-robust a posteriori error estimates of Prager-Synge type for Nédélec finite element approximations of the curl-curl problem. A divergence-free decomposition of a divergence-free H(div)-conforming piecewise polynomial, relying on over-constrained minimizations in Raviart-Thomas spaces, is the key ingredient. Numerical results illustrate the theoretical developments.
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Preprints, Working Papers, ...
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https://hal.inria.fr/hal-03227570
Contributor : Martin Vohralik Connect in order to contact the contributor
Submitted on : Monday, May 17, 2021 - 1:49:19 PM
Last modification on : Tuesday, May 17, 2022 - 3:20:54 AM
Long-term archiving on: : Wednesday, August 18, 2021 - 6:36:53 PM

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  • HAL Id : hal-03227570, version 1
  • ARXIV : 2105.07770

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Théophile Chaumont-Frelet, Martin Vohralík. p-robust equilibrated flux reconstruction in H(curl) based on local minimizations. Application to a posteriori analysis of the curl-curl problem. 2021. ⟨hal-03227570⟩

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