Journal of Scientific Computing

, Volume 68, Issue 2, pp 848–863 | Cite as

An Adaptive \(\varvec{P_1}\) Finite Element Method for Two-Dimensional Transverse Magnetic Time Harmonic Maxwell’s Equations with General Material Properties and General Boundary Conditions

  • S. C. BrennerEmail author
  • J. Gedicke
  • L.-Y. Sung


We present an adaptive \(P_1\) finite element method for two-dimensional transverse magnetic time harmonic Maxwell’s equations with general material properties and general boundary conditions. It is based on reducing the boundary value problems for Maxwell’s equations to standard second order scalar elliptic problems through the Hodge decomposition. We allow inhomogeneous and anisotropic electric permittivity, sign changing magnetic permeability, and both the perfectly conducting boundary condition and the impedance boundary condition. The optimal convergence of the adaptive finite element method is demonstrated by numerical experiments. We also present results for a semiconductor simulation, a cloaking simulation and a flat lens simulation that illustrate the robustness of the method.


Adaptivity Error estimators Finite element method Hodge decomposition Maxwell’s equations Impedance boundary condition Metamaterials Cloaking Flat lens 


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Mathematics, Center for Computation and TechnologyLouisiana State UniversityBaton RougeUSA
  2. 2.Interdisziplinäres Zentrum für Wissenschaftliches Rechnen (IWR)Universität HeidelbergHeidelbergGermany

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