We introduce a new numerical method for solving time-harmonic Maxwell’s equations via the modified weak Galerkin technique. The inter-element functions of the weak Galerkin finite elements are replaced by the average of the two discontinuous polynomial functions on the two sides of the polygon, in the modified weak Galerkin (MWG) finite element method. With the dependent inter-element functions, the weak curl and the weak gradient are defined directly on totally discontinuous polynomials. Optimal-order convergence of the method is proved. Numerical examples confirm the theory and show effectiveness of the modified weak Galerkin method over the existing methods.

中文翻译：

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多面体网格麦克斯韦方程组的修正弱伽辽金有限元法

我们引入了一种新的数值方法，通过改进的弱伽辽金技术来求解时谐麦克斯韦方程组。改进的弱伽辽金（MWG）有限元法中，弱伽辽金有限元的元间函数被多边形两侧的两个不连续多项式函数的平均值代替。利用依赖的元素间函数，弱旋度和弱梯度直接定义在完全不连续多项式上。证明了该方法的最优阶收敛性。数值例子证实了该理论，并显示了改进的弱伽辽金方法相对于现有方法的有效性。