An equilibrated a posteriori error estimator for arbitraryorder Nédélec elements for magnetostatic problems
Abstract
We present a novel \textit{a posteriori} error estimator for Nédélec elements for magnetostatic problems that is constantfree, i.e. it provides an upper bound on the error that does not involve a generic constant. The estimator is based on equilibration of the magnetic field and only involves small local problems that can be solved in parallel. Such an error estimator is already available for the lowestdegree Nédélec element [D. Braess, J. Schöberl, \textit{Equilibrated residual error estimator for edge elements}, Math. Comp. 77 (2008)] and requires solving local problems on vertex patches. The novelty of our estimator is that it can be applied to Nédélec elements of arbitrary degree. Furthermore, our estimator does not require solving problems on vertex patches, but instead requires solving problems on only single elements, single faces, and very small sets of nodes. We prove reliability and efficiency of the estimator and present several numerical examples that confirm this.
 Publication:

arXiv eprints
 Pub Date:
 September 2019
 arXiv:
 arXiv:1909.01853
 Bibcode:
 2019arXiv190901853G
 Keywords:

 Mathematics  Numerical Analysis;
 65N15;
 65N30;
 65N50
 EPrint:
 J. Sci. Comput. 83, 58 (2020)