A method to compute guaranteed lower bounds to the eigenvalues of the Maxwell system in two or three space dimensions is proposed as a generalization of the method of Liu and Oishi [SIAM J. Numer. Anal., 51, 2013] for the Laplace operator. The main tool is the computation of an explicit upper bound to the error of the Galerkin projection. The error is split in two parts: one part is controlled by a hypercircle principle and an auxiliary eigenvalue problem. The second part requires a perturbation argument for the right-hand side replaced by a suitable piecewise polynomial. The latter error is controlled through the use of the commuting quasi-interpolation by Falk--Winther and computational bounds on its stability constant. This situation is different from the Laplace operator where such a perturbation is easily controlled through local Poincar\'e inequalities. The practical viability of the approach is demonstrated in two-dimensional test cases.

翻译：在两个或三个空间维度中计算与Maxwell系统电子值的保障下限的低限的方法,建议作为Laplace操作员Laplace操作员Liu和Oishi[SIAM J.Numer. Anal., 51, 2013]方法的概括。主要工具是计算加勒金投影错误的明显上界。错误分为两部分:一部分受超环原理和辅助电子值问题控制。第二部分要求对右侧进行扰动论证,而右侧则由合适的片断聚氨酯替代。后一种错误通过使用Falk-Winther的通勤准内插法及其稳定性常态的计算边框加以控制。这种情况不同于Laplace操作员,后者很容易通过本地Poincar\'e的不平等加以控制。该方法的实际可行性在二维测试案例中得到证明。