  In many problems involving particle accelerators and relativistic plasmas,
the accurate modeling of relativistic particle motion is essential for accurate
physical predictions. Here, we extend a charge-conserving finite element
time-domain (FETD) particle-in-cell (PIC) algorithm for the time-dependent
Maxwell-Vlasov equations on irregular (unstructured) meshes to the relativistic
regime by implementing and comparing three particle pushers: (relativistic)
Boris, Vay, and Higuera-Cary. We illustrate the application of the proposed
relativistic FETD-PIC algorithm for the analysis of particle cyclotron motion
at relativistic speeds, harmonic particle oscillation in the Lorentz-boosted
frame, and relativistic Bernstein modes in magnetized charge-neutral (pair)
plasmas.
