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

Abstract 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 P 0 formulation of the Dirac spinor field. Numerical simulations are provided to show the efficiency of the method.

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