A Weak Galerkin Finite Element Method for the Maxwell Equations
A Weak Galerkin Finite Element Method for the Maxwell Equations
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DOI：
10.1007/s10915-014-9964-4
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发表时间：
2013-12
影响因子：
2.5
通讯作者：
Lin Mu;Junping Wang;X. Ye;Shangyou Zhang
中科院分区：
文献类型：
--
作者：
Lin Mu;Junping Wang;X. Ye;Shangyou Zhang
本文介绍了一种求解时谐麦克斯韦方程组的弱伽辽金（WG）有限元方法。WG有限元法基于两个算子：离散弱旋度和离散弱梯度，并具有适当定义的稳定化，以强制逼近函数的弱连续性。这种WG方法是高度灵活的，允许使用不连续的逼近函数的任意形状的多面体，在同一时间，是参数自由。本文给出了WG逼近在各种离散范数下的最优收敛阶。WG方法的一个有效的实施开发通过变量减少以下舒尔补的方法，产生一个系统的线性方程组，只涉及与元素边界相关的未知数。数值结果证实了理论的收敛性。
This paper introduces a numerical scheme for the time-harmonic Maxwell equations by using weak Galerkin (WG) finite element methods. The WG finite element method is based on two operators: discrete weak curl and discrete weak gradient, with appropriately defined stabilizations that enforce a weak continuity of the approximating functions. This WG method is highly flexible by allowing the use of discontinuous approximating functions on arbitrary shape of polyhedra and, at the same time, is parameter free. Optimal-order of convergence is established for the WG approximations in various discrete norms which are either-like orand-like. An effective implementation of the WG method is developed through variable reduction by following a Schur-complement approach, yielding a system of linear equations involving unknowns associated with element boundaries only. Numerical results are presented to confirm the theory of convergence.