Abstract
This paper adapts the weak Galerkin (WG) finite element scheme to Maxwell’s equations in the time domain. Developed by Wang and Ye in 2011, the WG scheme is a discontinuous Galerkin-like method that relies on a new notion of the discrete weak derivative. The WG method as applied to Maxwell’s equations uses a discrete weak curl and an extra stabilization term to enforce a weak continuity of the solution across elements. Semi-discrete and fully-discrete schemes are developed and are shown to be unconditionally stable. An optimal order of convergence is proven in an appropriate energy norm and confirmed by numerical results. For clarity, the theoretical analysis is carried out for 3-D case. Some details showing how to implement this WG scheme in 2-D are provided and numerical results are given in 2-D.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
