2020/02/25 by Théophile Chaumont-Frelet, Chaumont-Frelet, Théophile, Barbara Verfürth +1 · 1 citation
Computer Science · Engineering · Mathematics · #35J20 #65N12 #65N15 #65N30 #78A48 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Applied mathematics #Calculus (dental) #Class (philosophy) #Composite Material Mechanics #Computer science #Convergence (economics) #Element (criminal law) #Engineering #FOS: Mathematics #Finite element method #Law #Mathematical analysis #Mathematical optimization #Mathematics #Norm (philosophy) #Numerical Analysis (math.NA) #Physics #Political science #Sign (mathematics) #Structural engineering #cs.NA #math.NA #msc:35J20 #msc:65N12 #msc:65N15 #msc:65N30 #msc:78A48
paper · pdf · open access · doi:10.48550/arxiv.2002.10818
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2020/02/25 · arxiv created 2020/08/27 · arxiv updated 2020/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Problems with sign-changing coefficients occur, for instance, in the study of transmission problems with metamaterials. In this work, we present and analyze a generalized finite element method in the spirit of the Localized Orthogonal Decomposition, that is especially efficient when the negative and positive materials exhibit multiscale features. We derive optimal linear convergence in the energy norm independently of the potentially low regularity of the exact solution. Numerical experiments illustrate the theoretical convergence rates and show the applicability of the method for a large class of sign-changing diffusion problems.