Abstract.

An explicit, adaptive, hybrid finite element/finite difference method is proposed forthe numerical solution of Maxwell’s equations in the time domain. The method is hybrid in thesense that different numerical methods, finite elements and finite differences, are used in differentparts of the computational domain. Thus, we combine the flexibility of finite elements with theefficiency of finite differences. Furthermore, an a posteriori error estimate is derived for localadaptivity and error control inside the subregion, where finite elements are used. Numericalexperiments illustrate the usefulness of computational adaptive error control of proposed newmethod.

Keywords:

Maxwell’s equations, hybrid finite element/finite difference method, adaptive finiteelement methods, a posteriori error estimates, efficiency, reliability.