Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $p$-robust equilibrated flux reconstruction in ${\boldsymbol
  H}(\mathrm{curl})$ based on local minimizations. Application to a posteriori
  analysis of the curl-curl problem   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
N\'ed\'elec 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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The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: math-ph