This paper presents a posteriori error estimate for the weak Galerkin (WG) finite element method used to solve H(curl)-elliptic problems. Firstly, we introduce a WG method for solving H(curl)-elliptic problems and a corresponding residual type error estimator without a stabilization term. Secondly, we establish the reliability of the error estimator by demonstrating that the stabilization term is controlled by the error estimator. We also evaluate the efficiency of the error estimator using standard bubble functions. Finally, we present some numerical results to show the performances of the error estimator in both uniform and adaptive meshes.

中文翻译：

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H(curl)-椭圆问题的WG方法的后验误差估计

本文介绍了后验的用于求解弱伽辽金 (WG) 有限元法的误差估计H（卷曲）-椭圆问题。首先我们介绍一下WG方法来求解H(curl)-椭圆问题和相应的没有稳定项的残差类型误差估计器。其次，我们通过证明稳定项由误差估计器控制来建立误差估计器的可靠性。我们还使用标准气泡函数评估误差估计器的效率。最后，我们提出了一些数值结果来显示误差估计器在均匀网格和自适应网格中的性能。