Abstract
In this paper we present a numerical scheme to solve nonlinear Maxwell’s equations based on backward Euler discretization in time and curl-conforming finite elements in space. The nonlinearity is due to a field-dependent conductivity in the form of a power law. The system under study is hyperbolic and due to the nonlinear conductivity it lacks strong estimates of the second time derivative. We are able to prove convergence of our numerical scheme based on boundedness of the second derivative in the dual space. Convergence of the nonlinear term is based on the Minty–Browder technique. We also present the error estimate for the fully discretized problem and support the theory by some 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.
