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.

翻译：本文提出一种基于修正弱Galerkin技术求解时谐Maxwell方程组的新型数值方法。在修正弱Galerkin (MWG)有限元方法中，弱Galerkin有限元的单元间函数被替换为多边形两侧两个不连续多项式函数的平均值。通过这种依赖单元间函数的形式，弱旋度和弱梯度可直接定义于全不连续多项式空间上。本文证明了该方法的最优阶收敛性。数值算例验证了理论分析，并表明修正弱Galerkin方法相较于现有方法具有更高的计算效率。