SIAM Journal on Numerical Analysis, Volume 59, Issue 4, Page 2237-2253, January 2021.
We present an equilibration-based a posteriori error estimator for Nédélec element discretizations of the magnetostatic problem. The estimator is obtained by adding a gradient correction to the estimator for Nédélec elements of arbitrary degree presented in [Gedicke, Geevers, and Perugia, J. Sci. Comput., 83 (2020), pp. 1--23]. 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.

中文翻译：

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用于静磁问题的 Nédélec 离散化的多项式度稳健后验误差估计器

SIAM 数值分析杂志，第 59 卷，第 4 期，第 2237-2253 页，2021 年 1 月。
我们提出了一种基于平衡的后验误差估计器，用于静磁问题的 Nédélec 元素离散化。估计量是通过向 [Gedicke, Geevers, and Perugia, J. Sci.. 计算，83 (2020)，第 1--23 页]。这个新的估计器被证明是可靠的，可靠性常数为 1，并且是有效的，其效率常数与近似的多项式次数无关。这些特性在一系列三维测试问题的数值实验中得到了证明。