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. Journal of Scientific Computing, 83:1-23, 2020]. 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.

翻译：我们为磁体问题中的 N\'ed\'emec 元素的分解提出了一个基于后差差错估计仪。通过在[J. Gedicke, S. Gevers, 和 I. Perugia 中为任意学位的N\'ed\'emec 元素的估算器添加一个梯度校正,该估算器通过在[J. Gedicke, S. Gevers, 和 I. Perugia] 中为N\'ed\'emec 元素的分解来获取。一个基于后差差差错估计仪,用于磁体问题。《科学计算学期刊》,83: 1-23, 2020] 。这个新的估算器被证明是可靠的,可靠性常数1和高效,效率常数与近似的多元度无关。这些属性在三维测试问题的一系列数字实验中得到了证明。