We consider finite element discretizations of Maxwell’s equations coupled with a non-local hydrodynamic Drude model that accurately accounts for electron motions in metallic nanostructures. Specifically, we focus on a posteriori error estimation and mesh adaptivity, which is of particular interest since the electromagnetic field usually exhibits strongly localized features near the interface between metals and their surrounding media. We propose a novel residual-based error estimator that is shown to be reliable and efficient. We also present a set of numerical examples where the estimator drives a mesh adaptive process. These examples highlight the quality of the proposed estimator, and the potential computational savings offered by mesh adaptivity.

我们考虑了麦克斯韦方程组的有限元离散化与非局部流体动力学德鲁德模型相结合，该模型准确地解释了金属纳米结构中的电子运动。具体来说，我们专注于后验误差估计和网格自适应性，这是特别令人感兴趣的，因为电磁场通常在金属与其周围介质之间的界面附近表现出强烈的局部特征。我们提出了一种新的基于残差的误差估计器，它被证明是可靠和有效的。我们还提供了一组数值示例，其中估计器驱动网格自适应过程。这些示例突出了提议的估计器的质量，以及网格自适应提供的潜在计算节省。