A Time-Domain Finite Element Method for Maxwell's Equations

Presented here is a time-domain finite element method for approximating Maxwell's equations. The problem is to approximate the electromagnetic fields scattered by a bounded, inhomogeneous cavity embedded in an infinite ground plane. The time-dependent scattering problem is first discretized in time by Newmark's time-stepping scheme. The resulting semidiscrete problem is proved to be well posed. A nonlocal boundary condition on the cavity aperture is constructed to reduce the computational domain to the cavity itself. Stability analysis and error estimates of the fully discrete problem are provided.

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