We propose an arbitrary-order discontinuous Galerkin method for secondorder elliptic problem on general polygonal mesh with only one degree of freedom per element. This is achieved by locally solving a discrete least-squares over a neighboring element patch. Under a geometrical condition on the element patch, we prove an optimal a priori error estimates for the energy norm and for the L 2 norm. The accuracy and the efficiency of the method up to order six on several polygonal meshes are illustrated by a set of benchmark problems.
VO(2) films were fabricated on high-purity single-crystalline silicon substrate by the sol-gel method, followed by rapid annealing. The composition and microstructure of the films were investigated by X-ray photoelectron spectroscopy (XPS), X-ray diffraction (XRD), field-emission scanning electron microscopy (FE-SEM), and atomic force microscopy (AFM). The results indicated a polycrystalline nature with high crystallinity and compact nanostructure for the films, and the concentration of +4 valence vanadium is 79.85%. Correlated with these, a giant transmission modulation ratio about 81% of the film was observed by terahertz time domain spectroscopy. The experimentally observed transmission characteristics were reproduced approximately, by a simulation at different conductivities across the phase transition. According to the effective-medium theory, we assumed that it is important to increase the concentration of +4 valence vanadium oxide phases and improve the compactness of the VO(2) films for giant phase transition properties. The sol-gel-derived VO(2) films with giant phase transition properties at terahertz range, and the study on their composition and microstructure, provide considerable insight into the fabrication of VO(2) films for the application in THz modulation devices.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.