A polynomial-degree-robust a posteriori error estimator for Nédélec discretizations of magnetostatic problems

Joscha Gedicke, Sjoerd Geevers, Ilaria Perugia, Joachim Schöberl

Published 2020-04-17Version 1

We present an equilibration-based a posteriori error estimator for N\'ed\'elec element discretizations of the magnetostatic problem. The estimator is obtained by adding a gradient correction to the estimator for N\'ed\'elec elements of arbitrary degree presented in [J. Gedicke, S. Geevers, and I. Perugia. An equilibrated a posteriori error estimator for arbitrary-order N\'ed\'elec elements for magnetostatic problems. arXiv preprint, arXiv:1909.01853 [math.NA], 2019]. This new estimator is proven to be reliable, with reliability constant 1, and efficient, with an efficiency constant that is independent of the polynomial degree of the approximation. These properties are demonstrated in a series of numerical experiments on three-dimensional test problems.