Froidevaux, MarineGamst, Cornelia2021-12-172021-12-172016-11-302197-8085https://depositonce.tu-berlin.de/handle/11303/15861http://dx.doi.org/10.14279/depositonce-14634We study the propagation of light in a three-dimensional periodic photonic crystal, of which the electric permittivity is a complex nonlinear function of both space and frequency. We introduce the correct functional space needed to ensure that the operator corresponding to the weak formulation has a discrete spectrum, i.e., at most countably many isolated eigenvalues of finite multiplicity. Moreover, for two-dimensional photonic crystals, we present an a posteriori error estimator that can be used for the development of adaptive finite element methods.en510 MathematikMaxwell equationsphotonic crystalseigenvalue problemadaptive finite element methodposteriori error estimatorResearch Paper