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

We study extensions of piecewise polynomial data prescribed in a patch tetrahedra sharing an edge. show stability the sense that minimizers over spaces with tangential component jumps across faces and curl elements are subordinate broken energy norm to H ( mathvariant="bold">curl stretchy="false">) \boldsymbol H(\boldsymbol {\operatorname {curl}}) space same prescriptions. Our proofs constructive yield constants independent degree. then detail application this result posteriori error analysis curl–curl problem discretized Nédélec finite arbitrary order. The resulting estimators reliable, locally efficient, polynomial-degree-robust, inexpensive. They constructed by patchwise equilibration which, particular, does not produce globally -conforming flux. is only related edge patches can be realized without solutions problems sweep through around every mesh estimates become guaranteed when regularity pick-up constant explicitly known. Numerical experiments illustrate theoretical findings.