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Superconvergence analysis for time‐dependent Maxwell's equations in metamaterials
Author(s) -
Huang Yunqing,
Li Jichun,
Lin Qun
Publication year - 2012
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20703
Subject(s) - superconvergence , pointwise , mathematics , metamaterial , norm (philosophy) , partial differential equation , maxwell's equations , enhanced data rates for gsm evolution , element (criminal law) , mathematical analysis , finite element method , order (exchange) , physics , computer science , law , quantum mechanics , political science , thermodynamics , finance , economics , telecommunications
In this article, we consider the time‐dependent Maxwell's equations modeling wave propagation in metamaterials. One‐order higher global superclose results in the L 2 norm are proved for several semidiscrete and fully discrete schemes developed for solving this model using nonuniform cubic and rectangular edge elements. Furthermore, L ∞ superconvergence at element centers is proved for the lowest order rectangular edge element. To our best knowledge, such pointwise superconvergence result and its proof are original, and we are unaware of any other publications on this issue. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential 2011