Error analysis of implicit and exponential time integration of linear Maxwell's equations

Abstract

This thesis is concerned with the numerical analysis of some well-known time integration methods, such as implicit collocation methods and exponential integrators, for linear Maxwell's equations in time-domain. The error analysis of time integrators is done both for continuous Maxwell's equations in a semigroup theory framework and for space discrete problem obtained by discretizing Maxwell's equations in space by using discontinuous Galerkin finite element method.