Hybrid Discontinuous Finite Element/Finite Difference Method for Maxwell's Equations

A fully explicit, discontinuous hybrid finite element/finite difference method is proposed for the numerical solution of Maxwell's equations in the time domain. We call the method hybrid since the different numerical methods, interior penalty discontinuous finite element method, developed in [1], and finite difference method [2], are used in different parts of the computational domain. Thus, the flexibility of finite elements is combined with the efficiency of finite differences. Our numerical experiment illustrates stability of the proposed new method