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We study several numerical discretization techniques for the one-space plusone-time dimensional Dirac equation, including finite difference and space-timefinite element methods. Two finite difference schemes and several space-timefinite elements function spaces are analyzed with respect to known analyticsolutions. Further we propose a finite element discretization along theequations' characteristic lines, creating diamond-shaped elements in thespace-time plane. We show that the diamond shaped elements allow for physicallyintuitive boundary conditions, improve numerical efficiency, and reduce theoverall error of the computed solution as compared to the other finitedifference and space-time finite element discretizations studied in this paper.

A Study of Space-Time Discretizations for the Dirac Equation