论文标题
频率解释麦克斯韦方程不连续的盖尔金离散的后验错误估计
Frequency-explicit a posteriori error estimates for discontinuous Galerkin discretizations of Maxwell's equations
论文作者
论文摘要
我们为以一阶形式的时间谐波麦克斯韦方程的不连续的盖尔金离散化，提出了一个新的基于残差的后验误差估计器。我们确定估计器是可靠和有效的，并且分析和讨论了可靠性和效率常数对频率的依赖性。该提出的估计值概括了先前获得的相似结果，该结果已获得Helmholtz方程，并符合Maxwell方程的有限元离散化。另外，对于此处考虑的不连续的盖金（Galerkin）方案，我们还表明，对于平滑溶液，提出的估计量无稳定性。我们还提出了二维数字示例，这些示例突出了我们的关键理论发现，并建议拟议的估计器适合驱动$ h $ - 和$ hp $ $ $ $ $ - 适应性的迭代性修复。
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 discretization 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. We also present two-dimensional numerical examples that highlight our key theoretical findings and suggest that the proposed estimator is suited to drive $h$- and $hp$-adaptive iterative refinements.
