In this paper, we propose a weak Galerkin (WG) finite element method for the Maxwell eigenvalue problem. By restricting subspaces, we transform the mixed form of Maxwell eigenvalue problem into simple elliptic equation. Then we give the WG numerical scheme for the Maxwell eigenvalue problem. Furthermore, we obtain the optimal error estimates of arbitrarily high convergence order and prove the lower bound property of numerical solutions for eigenvalues. Numerical experiments show the accuracy of theoretical analysis and the property of lower bound.

翻译：本文针对麦克斯韦特征值问题提出了一种弱伽辽金有限元方法。通过子空间约束，将麦克斯韦特征值问题的混合形式转化为简单椭圆方程，继而建立了该问题的弱伽辽金数值格式。进一步地，我们获得了任意高阶收敛的最优误差估计，并证明了特征值数值解具有下界特性。数值实验验证了理论分析的精确性及下界特性。