English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We study extensions of piecewise polynomial data prescribed in a patch oftetrahedra sharing an edge. We show stability in the sense that the minimizersover piecewise polynomial spaces with prescribed tangential component jumpsacross faces and prescribed piecewise curl in elements are subordinate in thebroken energy norm to the minimizers over the broken H(curl) space with thesame prescriptions. Our proofs are constructive and yield constants independentof the polynomial degree. We then detail the application of this result to thea posteriori error analysis of the curl-curl problem discretized withN\'ed\'elec finite elements of arbitrary order. The resulting estimators arereliable, locally efficient, polynomial-degree-robust, and inexpensive. Theyare constructed by a broken patchwise equilibration which, in particular, doesnot produce a globally H(curl)-conforming flux. The equilibration is onlyrelated to edge patches and can be realized without solutions of patch problemsby a sweep through tetrahedra around every mesh edge. The error estimatesbecome guaranteed when the regularity pick-up constant is explicitly known.Numerical experiments illustrate the theoretical findings.

Stable broken H(curl) polynomial extensions and p-robust a posteriori error estimates by broken patchwise equilibration for the curl-curl problem