Time Domain Finite Element Method for Maxwell’s Equations

In this paper, we discuss a time domain finite element method for the approximate solution of Maxwell's equations. A weak formulation is derived for the electric and magnetic fields with appropriate initial and boundary conditions, and the problem is discretized both in space and time. In space, Nédeléc curl-conforming and Raviart-Thomas div-conforming finite elements are used to discretize the electric and magnetic fields, respectively. The backward Euler and symplectic schemes are applied to discretize the problem in time. For this system, we prove an error estimate. In addition, computational experiments are presented to validate the method, the electric and magnetic fields are visualized. The method also allows treating complex geometries of various physical systems coupled to electromagnetic fields in 3D.