We employ a finite-element (FE) solver with adaptive grid refinement to model hollow-core photonic crystal fibers (HC-PCFs) whose core is formed from 19 omitted cladding unit cells. We optimize the complete fiber geometry for minimal field intensity at material/air interfaces, which indicates low loss and high damage threshold, using multidimensional optimization. Our approach has very high numerical efficiency and accuracy, and we confirm that the FE-method is particularly well suited to model HC-PCFs. © The Authors. All rights reserved [DOI: 10.2971/jeos.2006.06011]