The quality of a local physical quantity obtained by the numerical method, such as the finite element method (FEM), attracts more and more attention in computational electromagnetism. Inspired by the idea of goal-oriented error estimate given for the Laplace problem, this work is devoted to a guaranteed a posteriori error estimate adapted for the quantity of interest (QOI) linked to magnetostatic problems, in particular, to the value of the magnetic flux density. The development is principally based on an equilibrated flux construction, which ensures fully computable estimators without any unknown constant. The main steps of the mathematical development are given in detail with the physical interpretation. An academic example using an analytical solution is considered to illustrate the performance of the approach, and a discussion about different aspects related to the practical point of view is proposed.

中文翻译：

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基于平衡通量重构的保证利率误差估计量

通过数值方法（例如有限元方法（FEM））获得的局部物理量的质量在计算电磁学中引起了越来越多的关注。受到针对拉普拉斯问题的面向目标的错误估计的想法的启发，这项工作致力于保证后验误差估计适用于与静磁问题有关的关注量（QOI），尤其是与磁通密度的值有关。该开发主要基于平衡通量构造，该构造可确保在没有任何未知常数的情况下可完全计算的估计量。通过物理解释详细给出了数学发展的主要步骤。考虑使用一个解析解决方案的学术示例来说明该方法的性能，并提出了与实际观点相关的不同方面的讨论。