Abstract
We present a finite element heterogeneous multiscale method for time-dependent Maxwell's equations in first-order formulation in highly oscillatory materials using Nédélec's edge elements. Based on a uniform approach for the error analysis of nonconforming space discretizations [D. Hipp, M. Hochbruck, and C. Stohrer, IMA J. Numer. Anal., 39 (2019), pp. 1206--1245], we prove an error bound for the semidiscrete scheme. We further present error bounds for the fully discrete scheme, where we consider time discretization using algebraically stable Runge--Kutta methods, the Crank--Nicolson method, and the leapfrog method. These error bounds are confirmed by numerical experiments.
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.
