SIAM Journal on Scientific Computing, Volume 43, Issue 4, Page B1008-B1028, January 2021.
The electro-quasistatic approximation of Maxwell equations is commonly used to model coupled resistive/capacitive phenomena at low frequencies. It neglects induction and becomes unstable in the stationary limit. We introduce a stabilization that prevents this low-frequency breakdown. It results in a system for the electric scalar potential that can be used for electro-quasistatics, electrostatics, as well as DC conduction. Our main finding is that the electro-quasistatic fields can be corrected for magnetic/inductive phenomena at any frequency in a second step. The combined field from both steps is a solution of the full Maxwell equations that consistently takes into account all electromagnetic effects. Electro-quasistatics serves as a gauge condition in this semidecoupled procedure to calculate the electromagnetic potentials. We derive frequency-stable weak variational formulations for both steps that (i) immediately lend themselves to finite-element Galerkin discretization, and (ii) can be equipped with the so-called electric circuit element (ECE) boundary conditions, which facilitate coupling with external circuit models.

中文翻译：

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电准静态规中的频率稳定全麦克斯韦

SIAM 科学计算杂志，第 43 卷，第 4 期，第 B1008-B1028 页，2021 年 1 月。
麦克斯韦方程的电准静态近似通常用于模拟低频下的耦合电阻/电容现象。它忽略感应并在静止极限中变得不稳定。我们引入了一种稳定性来防止这种低频击穿。它产生了一个可用于电准静态、静电以及直流传导的标量电势系统。我们的主要发现是，可以在第二步中针对任何频率下的磁/感应现象校正电准静态场。两个步骤的组合场是完整麦克斯韦方程的解，始终考虑所有电磁效应。在这个半解耦过程中，电准静态作为规范条件来计算电磁势。