SIAM Journal on Numerical Analysis, Volume 62, Issue 1, Page 400-421, February 2024.
Abstract. We propose a new residual-based a posteriori error estimator for discontinuous Galerkin discretizations of time-harmonic Maxwell’s equations in first-order form. We establish that the estimator is reliable and efficient, and the dependency of the reliability and efficiency constants on the frequency is analyzed and discussed. The proposed estimates generalize similar results previously obtained for the Helmholtz equation and conforming finite element discretizations of Maxwell’s equations. In addition, for the discontinuous Galerkin scheme considered here, we also show that the proposed estimator is asymptotically constant-free for smooth solutions.

中文翻译：

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麦克斯韦方程组间断伽辽金离散化的频率显式后验误差估计

SIAM 数值分析杂志，第 62 卷，第 1 期，第 400-421 页，2024 年 2 月。
摘要。我们提出了一种新的基于残差的后验误差估计器，用于一阶形式的时谐麦克斯韦方程组的不连续伽辽金离散化。我们确定估计器是可靠且高效的，并分析和讨论了可靠性和效率常数对频率的依赖性。所提出的估计概括了先前获得的亥姆霍兹方程和麦克斯韦方程的符合有限元离散化的类似结果。此外，对于这里考虑的不连续伽辽金方案，我们还表明所提出的估计量对于平滑解是渐近无常数的。