This paper presents a comparison of various particle-in-cell methodologies for numerical simulation of the Weibel instability. A convergence study with the established finite difference time domain particle-in-cell method establishes a base result. Comparison to novel particle-in-cell methods based on an implicit temporal discretization, and on a second and fifth order discontinuous Galerkin scheme (DG-PIC) provide insights into components of the DG-PIC schemes including divergence cleaning, particle weighing parameters and resolution requirements. High-order DG-PIC uses less grid points for a resolved solution making it competitive with the established finite difference method.