A simple and accurate mixed P0–Q1P0–Q1 solver for the Maxwell–Dirac equations

In this paper we propose and analyze a simple but accurate numerical method for solving the Maxwell–Dirac system for relativistic particles submitted to an external ultrashort intense pulse. Maxwell’s equations are solved using a second order finite element method in space and time. The Dirac equation solver is based on a method of characteristics with a P0P0 formulation of the Dirac spinor field. Numerical simulations are provided to show the efficiency of the method.