A Weak Galerkin Finite Element Method for the Maxwell Equations

作者：Mu, Lin^*; Wang, Junping; Ye, Xiu; Zhang, Shangyou

来源：Journal of Scientific Computing, 2015, 65(1): 363-386.

DOI：10.1007/s10915-014-9964-4

• Weak Galerkin
• Finite element methods
• Weak curl
• Weak gradient
• Maxwell equations
• Polyhedral meshes

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 or and -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.

• 出版日期2015-10
• 单位国家自然科学基金委员会